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  • 10 KB (1,498 words) - 14:47, 3 February 2024
  • Genetic algorithms (GAs) (also known as evolutionary algorithms [EAs]) assume a discrete search space $H$ and a function $f:H\to \R$. The [1] Back, T., Evolutionary Algorithms in Theory and Practice, Oxford University Press, 1996
    6 KB (958 words) - 06:10, 19 April 2013
  • ...connecting algorithms of a fixed type and expressing the fact that any two algorithms thus connected yield the same results if fed with the same given type of in ...he alphabet $A$, then the second algorithm also converts $P$ to $Q$. These algorithms are called completely equivalent with respect to $A$ if for any $P$ in $A$
    4 KB (663 words) - 12:42, 19 August 2014
  • $#C+1 = 33 : ~/encyclopedia/old_files/data/A011/A.0101910 Algorithms, theory of ...[Turing machine|Turing machine]]). Subsequent development of the theory of algorithms is due to the studies of Kleene, Post [[#References|[6]]], [[#References|[7
    19 KB (2,846 words) - 16:10, 1 April 2020
  • $#C+1 = 40 : ~/encyclopedia/old_files/data/A011/A.0101890 Algorithms, combinations of ...s for constructing new algorithms (cf. [[Algorithm|Algorithm]]) from given algorithms.
    6 KB (805 words) - 17:59, 1 April 2020
  • #REDIRECT [[Algorithms, theory of]]
    35 bytes (4 words) - 22:25, 30 November 2014
  • ...~/encyclopedia/old_files/data/O068/O.0608550 Optimization of computational algorithms ...possessing these properties. For this reason, in the theoretical study of algorithms one introduces a class of problems $ P $
    12 KB (1,798 words) - 20:07, 12 January 2024
  • ...ecial method for constructing algorithms based on the requirement that the algorithms should be exact or have an error of prescribed order of accuracy on some se
    4 KB (621 words) - 11:59, 12 August 2014

Page text matches

  • #REDIRECT [[Algorithms, theory of]]
    35 bytes (4 words) - 22:25, 30 November 2014
  • ...me alphabet, the concepts of equivalence and complete equivalence of these algorithms with respect to it can be naturally introduced. ...<TR><TD valign="top">[1]</TD> <TD valign="top"> A.A. Markov, "Theory of algorithms" , Israel Program Sci. Transl. (1961) (Translated from Russian) (Also: T
    2 KB (301 words) - 15:11, 24 December 2018
  • ...s [[Optimization of computational algorithms|optimization of computational algorithms]]. Sometimes, however, these concepts are treated differently. For example,
    634 bytes (96 words) - 17:07, 7 February 2011
  • ''for a given class of algorithms'' ...machines it is the universal [[Turing machine|Turing machine]], for normal algorithms it is the [[Universal normal algorithm|universal normal algorithm]], etc.
    1 KB (162 words) - 15:10, 3 August 2014
  • ...olutionary strategies; evolutionary programming; genetic programming. Such algorithms and ideas have found many applications in, e.g.: [[Scheduling theory|schedu ...r><td valign="top">[a5]</td> <td valign="top"> Z. Michalewicz, "Genetic algorithms $+$ data structures $=$ evolution programs" , Springer (1992)</td></tr><tr
    2 KB (296 words) - 16:58, 1 July 2020
  • ...ho, J.E. Hopcroft, J.D. Ullman, "The design and analysis of computer algorithms" , Addison-Wesley (1976)</TD></TR> <TR><TD valign="top">[a2]</TD> <TD valign="top"> S. Even, "Graph algorithms" , Computer Sci. Press (1979)</TD></TR>
    3 KB (440 words) - 21:26, 15 November 2014
  • ...basis of which lies a certain synthesis of ideas in the theory of sets and algorithms (see [[#References|[2]]]).
    1 KB (150 words) - 17:27, 7 February 2011
  • $#C+1 = 40 : ~/encyclopedia/old_files/data/A011/A.0101890 Algorithms, combinations of ...s for constructing new algorithms (cf. [[Algorithm|Algorithm]]) from given algorithms.
    6 KB (805 words) - 17:59, 1 April 2020
  • ...connecting algorithms of a fixed type and expressing the fact that any two algorithms thus connected yield the same results if fed with the same given type of in ...he alphabet $A$, then the second algorithm also converts $P$ to $Q$. These algorithms are called completely equivalent with respect to $A$ if for any $P$ in $A$
    4 KB (663 words) - 12:42, 19 August 2014
  • ...]] used in the numerical research into random processes and phenomena, and algorithms of the [[Monte-Carlo method|Monte-Carlo method]] for solving deterministic ...[#References|[4]]]). Particularly effective are those stochastic numerical algorithms that allow a number of realizations of the algorithm to be made simultaneou
    5 KB (649 words) - 17:24, 7 February 2011
  • ...t one to use small efficient algorithms as building blocks for larger-size algorithms [[#References|[a3]]]. ...ign="top">[a3]</TD> <TD valign="top"> R.C. Agarwal, J.W. Cooley, "New algorithms for digital convolution" ''IEEE Trans. Acoustics, Speech and Signal Proces
    3 KB (414 words) - 08:29, 6 June 2020
  • ...a sequence representation may define $2^l$ equivalence relations. Genetic algorithms implicitly process these relations in a very parallel manner and detect goo ...neration to generation through selection, crossover, and mutation. Genetic algorithms use such operators for detecting better relations and classes that finally
    6 KB (810 words) - 15:55, 10 July 2014
  • ...ithm of one kind or another — Turing machines, recursive functions, normal algorithms, and others — one may, by virtue of Church' thesis, restrict oneself to i
    3 KB (422 words) - 18:10, 12 December 2014
  • .... Zharov, "The complexity of a universal normal algorithm" , ''Theory of algorithms and mathematical logic'' , Moscow (1974) pp. 34–54 (In Russian)</TD></ ...lign="top"> A.A. Markov, N.M. [N.M. Nagornyi] Nagorny, "The theory of algorithms" , Kluwer (1988) pp. Chapt. V (Translated from Russian)</TD></TR></table
    2 KB (340 words) - 07:01, 27 May 2023
  • ...one of the fundamental results in the general theory of algorithms (cf. [[Algorithms, theory of]]); it may be (is) used in deriving all known negative results f
    1 KB (217 words) - 22:25, 30 November 2014
  • ...ed "theorems on universal algorithms" , dealing with the realizability of algorithms whose codings model the operation of any algorithm of this type. ...n arises — to wit, how to recognize self-applicable algorithms among other algorithms of this type — is not solvable by an algorithm of this type. This result
    4 KB (623 words) - 16:10, 1 April 2020
  • Three algorithms can perform this task. ...ty assumption [[#References|[a4]]]. A general perspective on probabilistic algorithms may be found in [[#References|[a5]]].
    5 KB (679 words) - 16:09, 1 April 2020
  • ...lign="top"> A.A. Markov, N.M. [N.M. Nagornyi] Nagorny, "The theory of algorithms" , Kluwer (1988) (Translated from Russian)</TD></TR></table>
    1 KB (227 words) - 19:42, 5 June 2020
  • * Ivan Rival (ed.), "Algorithms and Order", Kluwer (1989) {{ISBN|940107691X}} {{ZBL|0709.68004}}
    584 bytes (69 words) - 07:54, 19 March 2023
  • ...rier transform algorithms, such as the Cooley–Tukey fast Fourier transform algorithms {{Cite|CoTu}}, depend on the existence of non-trivial divisors of the trans ...m computations of prime power size $p^N$ and introduced cyclic convolution algorithms based on the polynomial version of the [[Chinese remainder theorem|Chinese
    4 KB (535 words) - 22:23, 25 April 2012
  • ...(ed.) ''The Schur complement and its applications'', Numerical Methods and Algorithms '''4''' Springer (2005) {{ISBN|0-387-24271-6}} {{ZBL|1075.15002}}
    467 bytes (70 words) - 12:24, 12 November 2023
  • A branch of mathematics and computer science concerned with finding efficient algorithms, or computational procedures, for solving geometric problems. Such problems ...metric configurations. It is impossible to list all important problems and algorithms of computational geometry, and some basic concepts and results are consider
    6 KB (957 words) - 17:46, 4 June 2020
  • ...to find primality proofs for numbers of $ 1000 $ decimal digits. For these algorithms, see the overview in [[#References|[a4]]] and the original references [[#Re ..."> E. Bach, J. Shallit, "Algorithmic number theory" , '''1: Efficient Algorithms''' , MIT (1996)</TD></TR>
    3 KB (485 words) - 22:01, 25 October 2014
  • ...D valign="top">[2]</TD> <TD valign="top"> N.M. Nagornyi, "The theory of algorithms" , Kluwer (1988) (Translated from Russian)</TD></TR></table>
    2 KB (337 words) - 22:11, 5 June 2020
  • ...ssical real numbers that are computable in some sense or other by means of algorithms. (See also [[Constructive analysis|Constructive analysis]].)
    571 bytes (88 words) - 16:54, 7 February 2011
  • The comparison of algorithms and the analysis of numerical problems in a Bayesian setting, cf. also [[Ba ...for inputs sharing some common properties. In a theoretical comparison of algorithms one either selects a class $P$ of inputs and defines the cost and the error
    6 KB (908 words) - 18:44, 21 March 2024
  • ...ociative calculus]]). The detailed definition and general theory of normal algorithms are set forth in [[#References|[1]]] (Chapts. I–V); see also [[#Reference ...riginal algorithm $\mathfrak A$. This convention is known in the theory of algorithms as the normalization principle. The formalization of the concept of an algo
    6 KB (927 words) - 15:08, 24 December 2018
  • ...ty, for designing and analyzing parallel combinatorial and graph-theoretic algorithms. The model focuses on the inherent level of computational parallelism witho ...n $O(\log n)$ time using $O(n)$ processors, parallel matrix multiplication algorithms running in $O(\log n)$ time using $O(n^3/\log n)$ processors, and string ma
    6 KB (940 words) - 23:19, 25 November 2018
  • ...(i.e. through schemes of general recursion). Let the complexity of normal algorithms and of Turing machines mean, respectively, the length of the encoding and t The study of the complexity of algorithms solving the finite restrictions of algorithmically unsolvable problems (the
    8 KB (1,158 words) - 16:10, 1 April 2020
  • ...tions has been an object of study in the [[Algorithms, theory of|theory of algorithms]] from the very beginning of its creation. In particular, this analogy lies
    2 KB (351 words) - 21:15, 29 January 2017
  • Genetic algorithms (GAs) (also known as evolutionary algorithms [EAs]) assume a discrete search space $H$ and a function $f:H\to \R$. The [1] Back, T., Evolutionary Algorithms in Theory and Practice, Oxford University Press, 1996
    6 KB (958 words) - 06:10, 19 April 2013
  • * Ivan Rival (ed.),"Algorithms and Order", Kluwer (1989) {{ISBN|940107691X}} {{ZBL|0709.68004}}
    630 bytes (98 words) - 19:32, 17 November 2023
  • ...ic countries. It is supposed to be a standard language for the exchange of algorithms between socialistic countries. It is based on the language Algol-60 (cf. [[ ..."top">[1]</TD> <TD valign="top"> "Description of the language ALGAMS" , ''Algorithms and algorithmic languages'' : 3 , Moscow (1968) pp. 3–56 (In Russian)
    2 KB (340 words) - 17:06, 7 February 2011
  • Some authors make a specific distinction between algorithms and procedures. Algorithms are prescriptions of sequences of actions which should always terminate aft
    3 KB (398 words) - 16:54, 7 February 2011
  • ...~/encyclopedia/old_files/data/O068/O.0608550 Optimization of computational algorithms ...possessing these properties. For this reason, in the theoretical study of algorithms one introduces a class of problems $ P $
    12 KB (1,798 words) - 20:07, 12 January 2024
  • ...e treated as an aspect of the [[idempotent correspondence principle]]. For algorithms, this heuristic principle means that "if one has an important and interest ...algorithms can often be approximated by linear ones. It is well-known that algorithms from linear algebra are convenient for parallel computations (see, e.g. [[#
    7 KB (1,079 words) - 20:39, 16 November 2023
  • ...osely connected with the theory of algorithms (cf. [[Algorithms, theory of|Algorithms, theory of]]), particularly so with the theory of abstract machines, since ...an automaton and that of obtaining corresponding estimates. Fairly simple algorithms have been developed for finite automata making it possible, with the aid of
    7 KB (975 words) - 18:49, 5 April 2020
  • ...rithm. Exact definitions of computable functions, effective procedures and algorithms were given in various forms by D. Hilbert, K. Gödel, A. Church, S.C. Kleen ...an algorithm are Turing machines, partial recursive functions, the normal algorithms of Markov, and others.
    18 KB (2,635 words) - 19:56, 5 September 2017
  • ..., "Separability with respect to invariants" , ''Studies on the theory of algorithms and mathematical logic'' , '''1''' , Moscow (1973) pp. 205–210 (In Rus
    3 KB (392 words) - 17:21, 7 February 2011
  • ...The following universal functions play an important role in the theory of algorithms: 1) universal partial recursive functions for the class of all $ n $- ...TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top"> A.I. Mal'tsev, "Algorithms and recursive functions" , Wolters-Noordhoff (1970) (Translated from Russ
    3 KB (435 words) - 13:01, 19 December 2020
  • ...TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> A.I. Mal'tsev, "Algorithms and recursive functions" , Wolters-Noordhoff (1970) (Translated from Russ
    1 KB (148 words) - 17:24, 7 February 2011
  • ...d decoding algorithms that are close in their possibilities to the optimal algorithms whose existence has been proved in the theory of information transmission. ...bed on an intuitive level and have no clear mathematical description. Such algorithms always include learning processes with respect to a list of objects that ar
    7 KB (993 words) - 17:28, 7 February 2011
  • In the theory of algorithms more special kinds of $tt$-reducibility are also considered, for instance b ...gn="top"> A.N. Degtev, "Reducibilities of tabular type in the theory of algorithms" ''Russian Math. Surveys'' , '''34''' : 3 (1979) pp. 155–192 ''Uspek
    3 KB (414 words) - 21:57, 16 January 2016
  • ...(ed.) ''The Schur complement and its applications'', Numerical Methods and Algorithms '''4''' Springer (2005) {{ISBN|0-387-24271-6}}{{ZBL|1075.15002}}
    759 bytes (114 words) - 12:25, 12 November 2023
  • ..., W.H. Payne, "Generalized feedback shift register pseudorandom number algorithms" ''J. ACM'' , '''20''' (1973) pp. 456–468</td></tr><tr><td valign="top
    11 KB (1,696 words) - 19:30, 8 February 2024
  • The use of adaptive algorithms is now (1998) very widespread across such varied applications as system ide The study of adaptive algorithms is generally made through the theory of [[Stochastic approximation|stochast
    8 KB (1,242 words) - 15:31, 1 July 2020
  • ...n the computational complexity of a problem; the analysis of all permitted algorithms together with the structure of a problem can provide lower bounds (cf. also Consider a computational model for uniform algorithms over a set $\Sigma$. Two prominent examples are
    7 KB (1,161 words) - 16:46, 1 July 2020
  • .../TD> <TD valign="top"> M. Minoux, "Mathematical programming: theory and algorithms" , Wiley (1986)</TD></TR>
    1 KB (173 words) - 08:52, 25 April 2016
  • ...hms with regular closure does not coincide with the set of actually stable algorithms, construction of a closed algorithm frequently helps in investigating the s ...>[6]</TD> <TD valign="top"> A.F. Shapkin, "Closure of two computational algorithms, based on the idea of orthogonalization" ''Zh. Vychisl. Mat. i Mat. Fiz.''
    4 KB (651 words) - 17:23, 14 February 2020
  • ...<TR><TD valign="top">[2]</TD> <TD valign="top"> A.A. Markov, "Theory of algorithms" , Israel Program Sci. Transl. (1961) (Translated from Russian) (Also: T
    1 KB (172 words) - 16:25, 1 May 2014
  • ...ly-increasing function from the natural numbers onto $A$. In the theory of algorithms the important characteristics of a direct counting of a set are recursivene
    1 KB (167 words) - 11:07, 17 March 2023
  • ...the transport problem and the assignment problem makes it possible to use algorithms that are more efficient than the [[Simplex method|simplex method]]. Some of ...<TD valign="top"> M. Grötschel, L. Lovász, A. Schrijver, "Geometric algorithms and combinatorial optimization" , Springer (1987)</TD></TR><TR><TD valign=
    3 KB (453 words) - 18:48, 5 April 2020
  • ...ersion of the first one. The methods of solution here consist of arbitrary algorithms and non-deterministic formally-describable procedures. ==Equivalent transformations of algorithms.==
    15 KB (2,362 words) - 18:45, 27 April 2014
  • ...discrete optimization problems are naturally formulated in terms of local algorithms. The starting theorems for local algorithms are the uniqueness theorem and the theorem on the existence of a best algor
    18 KB (2,562 words) - 18:06, 1 April 2020
  • ...many geometric and analytical properties. There are elegant and efficient algorithms for evaluation, differentiation, subdivision of the curves, and conversion ...s that allows exact representation of conic sections. These properties and algorithms make the curves popular in areas where shape is important. In addition to C
    5 KB (759 words) - 09:49, 27 March 2023
  • .... Combinatorial Gray codes are useful because they often lead to efficient algorithms for generating (i.e., listing) the objects. Some of the more important comb ...TD valign="top"> C.D. Savage, "Gray code sequences of partitions" ''J. Algorithms'' , '''10''' (1989) pp. 577–595</TD></TR><TR><TD valign="top">[a6]</TD>
    7 KB (1,089 words) - 19:42, 5 June 2020
  • ...hastic Lyapunov functions have been used to prove convergence of recursive algorithms driven by stochastic processes. Convergence problems of this type arise in ...Schuppen, "Convergence results for continuous-time stochastic filtering algorithms" ''J. Math. Anal. Appl.'' , '''96''' (1983) pp. 209–225</TD></TR></tab
    5 KB (718 words) - 04:11, 6 June 2020
  • A basic concept in the branch of the theory of algorithms called enumeration theory, which investigates general properties of classes ...ation of this idea it was noticed that many known results in the theory of algorithms turn out to be consequences of general regularities in enumeration theory.
    12 KB (1,899 words) - 19:37, 5 June 2020
  • ...of abstract computers by other classes (e.g. in order to simulate parallel algorithms by sequential ones). ...ty of their structure and also by the type of information processed by the algorithms. The main classes of abstract computers are listed below.
    9 KB (1,295 words) - 17:46, 4 June 2020
  • $#C+1 = 33 : ~/encyclopedia/old_files/data/A011/A.0101910 Algorithms, theory of ...[Turing machine|Turing machine]]). Subsequent development of the theory of algorithms is due to the studies of Kleene, Post [[#References|[6]]], [[#References|[7
    19 KB (2,846 words) - 16:10, 1 April 2020
  • ...programming language has a universal character, allowing one to formulate algorithms for solving various problems that are to be solved on different computers.
    4 KB (544 words) - 08:07, 6 June 2020
  • * Rajeev Motwani, Prabhakar Raghavan, "Randomized Algorithms", Cambridge University Press (1995) {{ISBN|978-0-521-47465-8}} {{ZBL|0849.6
    1 KB (173 words) - 07:29, 14 November 2023
  • ...ctionals. In discrete programming the algorithms employed are analogues of algorithms of local optimization, descent, random search, etc. For a review of approxi ...to find the extremum or a good approximation to it in the class of simple algorithms; this collection is often effectively described. This was first noted in so
    10 KB (1,391 words) - 12:30, 17 February 2021
  • ...such as the memory management aspects and computational complexity of such algorithms (cf. also [[Complexity theory]] and [[Algorithm, computational complexity o <TR><TD valign="top">[a3]</TD> <TD valign="top"> H. Edelsbrunner, "Algorithms in combinatorial geometry" , Springer (1987)</TD></TR>
    5 KB (738 words) - 19:10, 17 December 2015
  • <TR><TD valign="top">[1]</TD> <TD valign="top"> A.A. Markov, "Theory of algorithms" , Israel Program Sci. Transl. (1961) (Translated from Russian) (Also: T ...lign="top"> A.A. Markov, N.M. [N.M. Nagornyi] Nagorny, "The theory of algorithms" , Kluwer (1988) (Translated from Russian) {{ZBL|0663.03023}}</TD></TR>
    3 KB (544 words) - 07:12, 10 November 2023
  • ...used method for abbreviating proofs, and is often useful in improving the algorithms for the establishment of derivability. One of the most important results in
    1 KB (207 words) - 19:21, 17 October 2014
  • ...s present no difficulties). Also, rational numbers, algebraic polynomials, algorithms, and calculi of various well-defined types (cf. [[Algorithm|Algorithm]]; [[ ...lign="top"> A.A. Markov, N.M. [N.M. Nagornyi] Nagorny, "The theory of algorithms" , Reidel (1988) (Translated from Russian) {{ZBL|0663.03023}}</TD></TR>
    4 KB (587 words) - 20:53, 8 December 2015
  • There are efficient algorithms to solve this problem. Let $ X $ ...valign="top">[a9]</TD> <TD valign="top"> J. Kennington, R. Helgason, "Algorithms for network programming" , Wiley (1980)</TD></TR></table>
    7 KB (1,074 words) - 20:15, 15 March 2023
  • ...mathematical logic — the theory of algorithms (cf. [[Algorithms, theory of|Algorithms, theory of]]). The growing stream of information and the related problems o ...re of discrete analysis, related to problems in finite structures, is that algorithms by which these problems may be solved exist in most cases, while in classic
    9 KB (1,264 words) - 16:56, 15 April 2012
  • * Eric Bach, Jeffrey O. Shallit, ''Algorithmic Number Theory: Efficient algorithms, Volume 1'', MIT Press (1996) {{ISBN|0262024055}}
    1 KB (186 words) - 16:57, 25 November 2023
  • ...been constructed, based on certain intuitive principles, i.e. families of algorithms for solving classification problems. The most widely used are: models based ...ication is a priori known. In developing the general theory of recognition algorithms the most complete results have been obtained within an algebraic framework.
    8 KB (1,189 words) - 13:43, 17 April 2014
  • ...<TR><TD valign="top">[1]</TD> <TD valign="top"> A.A. Markov, "Theory of algorithms" , Israel Program Sci. Transl. (1961) (Translated from Russian) (Also: T
    2 KB (216 words) - 17:08, 7 February 2011
  • One of the basic concepts in the [[Algorithms, theory of|theory of algorithms]] and its applications. Its background was the fact that solvability (and u ...so-called priority method, which is extensively employed in the theory of algorithms.
    6 KB (862 words) - 19:26, 22 January 2016
  • ...ecial method for constructing algorithms based on the requirement that the algorithms should be exact or have an error of prescribed order of accuracy on some se
    4 KB (621 words) - 11:59, 12 August 2014
  • ...[[Automatic programming|automatic programming]] and for the publication of algorithms (it is an abbreviation of "ALGOrithmic Language" ). ...lly refers to "Algol-60" . It is especially suited for the description of algorithms of numerical analysis. The language is machine-independent and does not pro
    4 KB (632 words) - 17:21, 7 February 2011
  • ...]. The Scarf algorithm and other related ones rapidly evolved into various algorithms for solving equations, for finding extrema and for tracing bifurcating solu ...as a very extensive bibliography. A substantial number of previously known algorithms for solving equations can be obtained as particular cases of the homotopy c
    9 KB (1,325 words) - 17:26, 7 February 2011
  • ...nald E. Knuth, ''The Art of Computer Programming, Volume 4A: Combinatorial Algorithms, Part 1'', Addison-Wesley (2014) {{ISBN|0133488853}}
    1 KB (199 words) - 14:15, 12 November 2023
  • there are algorithms which are particularly convenient in practice. There is a considerable numb ...>[a4]</TD> <TD valign="top"> D.F. Elliot, K.R. Rao, "Fast transforms: algorithms, analysis, applications" , Acad. Press (1982)</TD></TR>
    4 KB (602 words) - 14:32, 17 March 2023
  • ...computable functions and theory of algorithms (cf. [[Algorithms, theory of|Algorithms, theory of]]; [[Computable function|Computable function]]) is any mapping o
    6 KB (919 words) - 08:26, 6 June 2020
  • * Rajeev Motwani, Prabhakar Raghavan, "Randomized Algorithms", Cambridge University Press (1995) {{ISBN|978-0-521-47465-8}} {{ZBL|0849.6
    1 KB (226 words) - 07:28, 14 November 2023
  • ...o [[Optimization of computational algorithms|Optimization of computational algorithms]]; [[Index transform|Information-based complexity]]; [[Curse of dimension|C ...gn="top"> G.W. Wasilkowski, H. Woźniakowski, "Weighted tensor-product algorithms for linear multivariate problems" ''Preprint'' (1998)</td></tr><tr><td va
    8 KB (1,086 words) - 17:43, 1 July 2020
  • ...first such algorithm was proposed by H. Scarf, [[#References|[a3]]]. Such algorithms later developed in the so-called homotopy or continuation methods for calcu ...n="top">[a4]</TD> <TD valign="top"> S. Karamadian (ed.) , ''Fixed points. Algorithms and applications'' , Acad. Press (1977)</TD></TR>
    4 KB (586 words) - 11:27, 17 March 2023
  • The accuracy of the algorithms based on the interpolation formulas of Lagrange, Newton and others strongly ...tly smooth and if the number of nodal points is large [[#References|[1]]]. Algorithms of numerical differentiation involving spline-interpolation [[#References|[
    5 KB (779 words) - 19:35, 5 June 2020
  • ...</TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> H. Edelsbrunner, "Algorithms in combinatorial geometry" , Springer (1987)</TD></TR><TR><TD valign="top"
    2 KB (247 words) - 17:32, 5 June 2020
  • ...tape scanned by the head of the machine. Time and storage costs for normal algorithms (cf. [[Normal algorithm|Normal algorithm]]), iterative arrays, multi-head a better than other algorithms" . However, as exemplified by the speed-up theorem (see below), such a form
    16 KB (2,413 words) - 16:10, 1 April 2020
  • 1) Provide algorithms turning $ R [ {\mathcal X} ] $ By keeping track of intermediate results in the algorithms, it is possible to express the Gröbner basis $ C $
    10 KB (1,471 words) - 14:52, 30 May 2020
  • ...theory of calculi is the theory of algorithms (cf. [[Algorithms, theory of|Algorithms, theory of]]). This is clear from the fact that the notion of a calculus is ...<TR><TD valign="top">[2]</TD> <TD valign="top"> A.A. Markov, "Theory of algorithms" , Israel Program Sci. Transl. (1961) (Translated from Russian) (Also: T
    8 KB (1,204 words) - 18:51, 13 November 2014
  • ...to use approximate solution methods of (2) in order to construct iteration algorithms for solving equation (1) (cf. [[Iteration algorithm|Iteration algorithm]]). ...m state is the desired optimum. Again this leads to all kinds of iteration algorithms, as in [[#References|[a3]]].
    4 KB (649 words) - 05:25, 19 March 2022
  • <TR><TD valign="top">[2]</TD> <TD valign="top"> A.I. Mal'tsev, "Algorithms and recursive functions" , Wolters-Noordhoff (1970) (Translated from Russ
    2 KB (250 words) - 20:46, 23 November 2023
  • ...m the previous one, usually by a small amount. The convergence analysis of algorithms like (a7) is treated in e.g. [[#References|[a6]]], [[#References|[a1]]], [[ ...</td> <td valign="top"> V. Solo, X. Kong, "Adaptive signal processing algorithms" , Prentice-Hall (1995)</td></tr></table>
    7 KB (1,131 words) - 14:45, 16 December 2023
  • ...t in real problems the computations may be too laborious. If so, heuristic algorithms are used to generate better patterns: as a rule, it is enough to consider c ...isted. For linear and rectangular parts applicable heuristic approximation algorithms have been programmed (see [[#References|[2]]]).
    8 KB (1,179 words) - 17:25, 27 October 2014
  • ...algorithms to test primality of numbers and, if composite, to factor them. Algorithms of this kind which can handle numbers of 100 or 200 digits have recently at
    6 KB (955 words) - 19:40, 1 November 2023
  • ...rocedures that solve every instance of the problem? Which problems possess algorithms for their solution? ...ion is of definite practical significance: One should not try to construct algorithms for an unsolvable problem. (There are some notorious examples of such attem
    13 KB (2,014 words) - 20:35, 31 December 2018
  • This approach makes it possible to construct numerical algorithms for a wide class of differential equations, including partial differential ...polation of operators and functionals in the construction of computational algorithms for solving concrete problems is based on the use of interpolation formulas
    26 KB (3,882 words) - 22:13, 5 June 2020
  • ...heorem, one asks to find these factors algorithmically, and to devise such algorithms with low cost. ...lled polynomial representation of $\sigma$ as its basic tool. The last two algorithms are based on Gauss' theorem that $x ^ { q ^ { d } } - x$ is the product of
    12 KB (1,739 words) - 13:11, 26 March 2023
  • ...le computation one has to use specialized [[Software|software]]. To encode algorithms on a computer, special language means are required. These are also consider
    2 KB (270 words) - 17:01, 7 February 2011
  • .... As shown in [[#References|[a3]]], this suffices to guarantee linear-time algorithms for many otherwise hard graph problems when instances are confined to Halin ...Borie, R.G. Parker, C.A. Tovey, "Automatic generation of linear-time algorithms from predicate calculus descriptions of problems on recursively constructed
    5 KB (722 words) - 20:45, 16 March 2023
  • * Donald E. Knuth, "Introduction to combinatorial algorithms and Boolean functions", ser. The Art of Computer Programming 4.0 (2008) pp.
    2 KB (261 words) - 18:11, 14 October 2023
  • ...for the modern precise statement of this problem as given by the theory of algorithms (cf. [[Church thesis|Church thesis]]). Other examples of such group calculi ...lign="top"> A.A. Markov, N.M. [N.M. Nagornyi] Nagorny, "The theory of algorithms" , Kluwer (1988) (Translated from Russian)</TD></TR></table>
    9 KB (1,334 words) - 19:42, 5 June 2020
  • ...nts take the values 0 or 1 only. Conditions a) and b) enable one to devise algorithms for the solution of the transportation problem that are essentially simpler The best known of these algorithms are the method of potentials and the so-called Hungarian method. The method
    5 KB (746 words) - 14:56, 7 June 2020
  • ...rogram, i.e. a collection of machine commands describing the computational algorithms, organizing the realization of the computational process in the given compu ...onal steps, method of]]). An important task in the theory of computational algorithms is their optimization.
    10 KB (1,642 words) - 08:41, 29 August 2014
  • Already in the Middle Ages a number of algorithms for constructing magic squares of odd order $ n $ Many algorithms for constructing magic squares are known (resulting in squares with non-lin
    5 KB (762 words) - 19:27, 12 January 2024
  • ..."A space-efficient on-line method of computing quantile estimators" ''J. Algorithms'' , '''2''' (1981) pp. 164–177</TD></TR></table>
    2 KB (281 words) - 17:22, 7 February 2011
  • ...n="top"> J.P. Duval, "Factorizing words over an ordered alphabet" ''J. Algorithms'' , '''4''' (1983) pp. 363–381</TD></TR>
    6 KB (946 words) - 13:41, 20 March 2023
  • ...se of development of the theory of algorithms (cf. [[Algorithms, theory of|Algorithms, theory of]]), there emerged a number of modifications of the original defi ===Representing Algorithms by Turing Machines===
    14 KB (2,355 words) - 12:40, 28 December 2013
  • ...is proved by providing exponentially large lower bounds that hold for all algorithms. Many problems suffer from the curse of dimension. Examples include numeric ...o [[Optimization of computational algorithms|Optimization of computational algorithms]]. Whether a problem suffers from the curse of dimension depends on the exa
    12 KB (1,706 words) - 20:29, 9 December 2023
  • ...nce, or they may vary during the calculation. For this reason, one designs algorithms that enable one to use grids that are more closely spaced in such zones. In order to set up reliable numerical algorithms, the problem of constructing a grid is often formulated as a task of minimi
    5 KB (759 words) - 10:59, 16 April 2014
  • ...>[a3]</TD> <TD valign="top"> J.M. Robertson, W.A. Webb, "Cake-cutting algorithms: be fair if you can" , A.K. Peters (1998)</TD></TR><TR><TD valign="top">[a
    2 KB (317 words) - 16:50, 30 December 2018
  • ...ly analyzed as well as implemented. Especially, primal-dual interior-point algorithms (i.e., methods generating primal and dual solutions in each iteration) prov ...ign="top"> Yu. Nesterov, A.S. Nemirovskii, "Interior point polynomial algorithms in convex programming" , ''Studies in Applied Mathematics'' , '''13''' , SI
    5 KB (710 words) - 22:13, 5 June 2020
  • .../TD> <TD valign="top"> M. Minoux, "Mathematical programming: theory and algorithms" , Wiley (1986)</TD></TR></table>
    3 KB (372 words) - 08:07, 22 November 2014
  • ...includes, in particular, the self-scaling variable metric algorithms (SSVM algorithms), which share most properties of the Broyden family and automatically compe ...op"> S.S. Oren, D.G. Luenberger, "Self-scaling variable metric (SSVM) algorithms I" ''Management Science'' , '''20''' (1974) pp. 845–862</td></tr><tr><
    12 KB (1,897 words) - 19:37, 9 February 2024
  • ...[[Network|network]] or [[Graph|graph]] that satisfy a given property. Such algorithms are also used, e.g., to optimize a function on a graph or network or on a s There is an obvious analogous search algorithm for non-oriented graphs. These algorithms run in $ O ( \# V + \# E ) $
    11 KB (1,442 words) - 08:12, 6 June 2020
  • In practice, time-consuming scanning is combined with algorithms for finding a local extremum: by scanning and a priori reduction of $ f ( 1) Algorithms of the heavy-sphere type (cf. [[Heavy sphere, method of the|Heavy sphere, m
    9 KB (1,335 words) - 08:01, 6 June 2020
  • ...and hence the Berlekamp–Massey algorithm, has connections to several other algorithms, most notably the extended [[Euclidean algorithm|Euclidean algorithm]] [[#R ...gorithms in numerical analysis such as Lanczos recursion and Levinson–Shur algorithms for Toeplitz matrices, as well as problems of minimal realizations in syste
    8 KB (1,155 words) - 18:48, 26 January 2024
  • ...TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> H. Edelsbrunner, "Algorithms in combinatorial geometry" , Springer (1987) {{MR|0904271}} {{ZBL|0634.5200
    2 KB (301 words) - 08:28, 6 June 2020
  • Hierarchical clustering algorithms can be characterized as ''greedy'' The algorithms, which have the potential for ''exactly'' replicating
    13 KB (1,912 words) - 18:57, 7 March 2024
  • ...estimate of the complexity of the amount of work and the specification of algorithms (see also [[Algorithmic information theory|Algorithmic information theory]] ...hnik, "On the unsolvability of the reducibility problem in the theory of algorithms" ''Dokl. Akad. Nauk SSSR'' , '''108''' : 2 (1956) pp. 194–197 (In Ru
    6 KB (921 words) - 17:32, 5 June 2020
  • ...recent survey of the simplex algorithm, the Karmarkar algorithm (interior algorithms) and ellipsoid methods in relation to each other, cf. [[#References|[a8]]]. ...p">[a6]</TD> <TD valign="top"> A.R.G. Heesterman, "Matrices and simplex algorithms" , Reidel (1983)</TD></TR><TR><TD valign="top">[a7]</TD> <TD valign="top">
    8 KB (1,246 words) - 06:35, 7 May 2022
  • A method of defining functions studied in the theory of algorithms and other branches of mathematical logic. This method has been used for a l ...nition of recursion consists not only in its significance in the theory of algorithms, but also in that it permits one to look from an "algorithmic" (in the ge
    13 KB (2,044 words) - 08:10, 6 June 2020
  • factorization. Such decompositions play an important role in numerical algorithms, [[#References|[a2]]], [[#References|[a3]]] (for instance, in computing eig
    2 KB (350 words) - 08:26, 6 June 2020
  • ...of [[Refal|Refal]], Snobol has its own theoretical premise, Markov normal algorithms (cf. [[Normal algorithm|Normal algorithm]]), in which the basic computing o ...rs. The implementation of this language aided the development of efficient algorithms for manipulating lines of variable length in a computer memory.
    6 KB (915 words) - 08:14, 6 June 2020
  • ...s [[Optimization of computational algorithms|Optimization of computational algorithms]].
    6 KB (871 words) - 17:45, 1 July 2020
  • <TR><TD valign="top">[2]</TD> <TD valign="top"> A.I. Mal'tsev, "Algorithms and recursive functions" , Wolters-Noordhoff (1970) (Translated from Russ
    2 KB (371 words) - 21:13, 2 November 2014
  • ...t the algorithm sought need not exist at all. As a result, the approach to algorithms on the part of mathematicians underwent a radical change, and new algorithm ...evertheless, since it makes it possible to speak of unsolvability of given algorithms in a wide sense, which is generally understood by mathematicians.
    21 KB (3,264 words) - 06:46, 26 March 2023
  • ...es are not always solvable according to Nash or strongly solvable. Various algorithms are available to find equilibrium solutions in bimatrix games: a method of
    2 KB (351 words) - 07:37, 23 August 2014
  • The various service algorithms produce quite diverse forms of queues. The simplest ones are presented belo .... These are associated with more complicated control sequences and service algorithms.
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  • ...more rigorous requirement as well: It is possible to tell, with the aid of algorithms, whether $P_0$ is deducible from $P_1,\ldots,P_l$ by one application of the
    3 KB (431 words) - 19:19, 17 October 2014
  • ...apparatus, and pseudo-random numbers, being constructed using arithmetical algorithms. It is usually assumed (for better or worse reason) that the sequence obtai ...od]]), and in cryptography, for the concrete realization of non-determined algorithms and behaviour predicted only "on the average" . For example, if the next
    6 KB (899 words) - 08:09, 6 June 2020
  • since the number of operations required increases rapidly. Many other algorithms have therefore been constructed, which, however, are not effectively applic ...ormal form is a natural way of improving the effectiveness of minimization algorithms. A conjunction should be eliminated (or, on the contrary, retained until th
    22 KB (3,328 words) - 08:31, 26 March 2023
  • ==Algorithms== ...se. The content of this term depends on the possibilities of computational algorithms and on the characteristics of the computer employed, such as the amount of
    12 KB (1,882 words) - 22:25, 1 September 2016
  • ...n)$ steps using $n$ processors. The relative simplicity of parallelization algorithms for expressions allows one to realize them automatically on a computer usin ...devices, etc.). On this level, automatic parallelization requires complex algorithms for the analysis of problems and has to take into account dynamic situation
    11 KB (1,714 words) - 03:17, 5 June 2016
  • ...amines and classifies subsets of natural numbers from the point of view of algorithms, and also studies the structures arising as a result of such a classificati ...TD></TR><TR><TD valign="top">[8]</TD> <TD valign="top"> A.I. Mal'tsev, "Algorithms and recursive functions" , Wolters-Noordhoff (1970) (Translated from Russ
    16 KB (2,323 words) - 08:10, 6 June 2020
  • [[Category:Algorithms]]
    2 KB (387 words) - 15:16, 20 November 2014
  • ...utations is exploited in order to devise very effective numerical solution algorithms. Famous special cases are the Hilbert matrix and Hilbert–Hankel operator, ...ction to the theory of formal orthogonal polynomials in the context of the algorithms of numerical analysis, including Lanczos' tridiagonalization process, ratio
    14 KB (2,126 words) - 16:45, 1 July 2020
  • Among the well-known extrapolation algorithms, there is also the $h^2$. Note that, sometimes, extrapolation algorithms are able to sum
    11 KB (1,808 words) - 21:52, 5 March 2012
  • ...ddition, subtraction, multiplication and division are algorithms; in these algorithms the possible results are non-negative integers written in the decimal syste ...eneral graphs. Intuitively, the least requirement on inputs and results of algorithms is that they must be constructive objects (cf. [[Constructive object|Constr
    18 KB (2,796 words) - 19:10, 11 December 2020
  • .... The term is often understood to mean the theory of numerical methods and algorithms for the solution of typical mathematical problems. This meaning was in fact ...lysis of mathematical models. The second is the development of methods and algorithms for solving typical mathematical problems involved in the investigation of
    13 KB (1,892 words) - 20:11, 31 December 2018
  • ...esses is presented in [[#References|[a5]]]. For applications of prediction algorithms in the applied sciences see [[#References|[a1]]].
    6 KB (908 words) - 08:23, 6 June 2020
  • ...a3]]], [[#References|[a5]]], [[#References|[a9]]]. Most of these automatic algorithms use one or several estimates for $R_n$ of the type (a4), which often are ob
    7 KB (1,043 words) - 19:57, 4 February 2024
  • ...gorithms such as Monte-Carlo methods, stochastic particle methods, ergodic algorithms, etc. (cf. also [[Differential equation, partial|Differential equation, par ...particles are dependent. For theoretical aspects related to probabilistic algorithms for partial differential equations, including the [[Boltzmann equation|Bolt
    9 KB (1,338 words) - 08:01, 6 June 2020
  • In economic algorithms for the inversion of Toeplitz matrices (see [[#References|[3]]], for exampl ...plitz matrices by vectors and a subtraction of vectors. There are economic algorithms for the multiplication of Toeplitz matrices by vectors, requiring (for orde
    11 KB (1,584 words) - 22:13, 5 June 2020
  • ...lign="top">[5]</TD> <TD valign="top"> A.I. Orlov, "On the comparison of algorithms for classifying by results observations of actual data" ''Dokl. Moskov. Ob
    3 KB (370 words) - 20:32, 16 January 2024
  • ...<TR><TD valign="top">[2]</TD> <TD valign="top"> A.A. Markov, "Theory of algorithms" , Israel Program Sci. Transl. (1961) (Translated from Russian) (Also: T
    3 KB (386 words) - 22:13, 5 June 2020
  • ...are usually called descent methods. The third group of methods consists of algorithms which use second derivatives of the functional.
    3 KB (434 words) - 08:00, 6 June 2020
  • ...erties of this method include the simplicity and the natural nature of its algorithms, as well as the fact that modifications can be made in the light of new inf ...ies of the particles: neutrons, photons, gamma-quanta, electrons, etc. The algorithms of statistical modelling for solving problems of atmospheric optics (see [[
    7 KB (1,015 words) - 17:27, 7 February 2011
  • ...al problems are simpler and practically more convenient than the available algorithms for solving the same problems for partial differential equations. The varia
    7 KB (969 words) - 17:33, 5 June 2020
  • ...ho, J.E. Hopcroft, J.D. Ullman, "The design and analysis of computer algorithms" , Addison-Wesley (1976)</TD></TR> ...="top">[a3]</TD> <TD valign="top"> M. Gondran, M. Minoux, "Graphes et algorithms" , Ed. Eyrolles (1979; 1988)</TD></TR>
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  • This approach to constructing computation algorithms can be extended to problems of hydrodynamics with heat conduction, to elast
    3 KB (431 words) - 10:52, 16 April 2014
  • ...l complexity, or the complexity of some specific but practically important algorithms and problems. One is referred to [[#References|[a5]]]–[[#References|[a7]] have no best algorithms: For every person's favourite algorithm $ f _ {i} $,
    20 KB (3,105 words) - 17:46, 4 June 2020
  • ...both false accepts and rejects, i.e. false answers at all, one has to use algorithms belonging to the complexity class $\mathrm{ZPP}$. In the same way, algorithms belonging to the complexity class $\mathrm{coRP}$ can be modified.
    12 KB (1,954 words) - 17:47, 26 December 2013
  • ...<TR><TD valign="top">[2]</TD> <TD valign="top"> A.A. Markov, "Theory of algorithms" , Israel Program Sci. Transl. (1961) (Translated from Russian) (Also: T
    3 KB (462 words) - 20:23, 31 July 2014
  • ...ective computational procedure is suitably formalized, as in the theory of algorithms.
    3 KB (490 words) - 22:33, 10 January 2016
  • ...ntionally called algorithms (in the present context, one is concerned with algorithms operating on words). ...treatment of existential statements leads to the necessity of considering algorithms. The assertion that a constructive objects with a given property exists, th
    20 KB (2,913 words) - 07:40, 14 August 2023
  • Algorithms are known for finding all classes of boundary forms. In particular, the Vor
    3 KB (421 words) - 22:10, 5 June 2020
  • ...f. [[Recursive function|Recursive function]]) is realized in the theory of algorithms. One of the general methods for constructing such hierarchies is based on d ...]</TD> <TD valign="top"> , ''Problems of mathematical logic. Complexity of algorithms and of classes of computable functions'' , Moscow (1970) (In Russian; tra
    9 KB (1,244 words) - 22:10, 5 June 2020
  • ...of programming them relies, to a large extent, on ideas from the theory of algorithms and mathematical cybernetics. In turn, practical work with computers poses ...valign="top">[5]</TD> <TD valign="top"> , ''Complexity of computations and algorithms'' , Moscow (1974) (In Russian; translated from English) (Collection of t
    18 KB (2,656 words) - 04:11, 6 June 2020
  • ...ity of an|Algorithm, computational complexity of an]]). In practice, exact algorithms are used for solving only moderately sized problem instances. This results ...M.G.C. Resende, "Parallel search for combinatorial optimization: genetic algorithms, simulated annealing, tabu search and GRASP" , ''Lecture Notes in Computer
    10 KB (1,422 words) - 08:14, 6 June 2020
  • ...e algorithms of variable directions have been proposed and examined. These algorithms are economic in the sense that the number of arithmetic operations necessar
    18 KB (2,500 words) - 06:21, 12 October 2023
  • ...hich connect this pair of vertices. Criteria have been found and effective algorithms have been developed for the establishment of the degree of connectivity of cf. [[Flow in a network|Flow in a network]]). Various effective algorithms for finding the maximum flow have been developed.
    13 KB (1,976 words) - 20:08, 15 March 2023
  • A method for obtaining a class of iteration algorithms (cf. [[Iteration algorithm|Iteration algorithm]]) for finding a simple real
    3 KB (505 words) - 14:56, 14 February 2020
  • ...decoding|coding and decoding]]; [[Combinatorics|combinatorics]]; geometric algorithms, and other areas.
    3 KB (421 words) - 22:15, 5 June 2020
  • ...ence are usually described by a transitive anti-reflexive binary relation. Algorithms for the evaluation of characteristics of large partially ordered sets of jo ...ical programming]] are often applicable to the development of optimization algorithms of this kind. Work on $ {\mathcal N} {\mathcal P} $-
    21 KB (3,117 words) - 10:04, 18 February 2021
  • ...tic translation]]). In mathematical linguistics methods of the theories of algorithms, automata and algebra are widely used. Keeping its applied sense, mathemati ...Therefore it is suitable not to construct deterministic effective systems (algorithms) but to construct non-deterministic systems (calculi), which allow either f
    14 KB (2,122 words) - 17:14, 3 November 2014
  • The practical search of extrema uses iterative algorithms of the form: ...and parallel computation of an extremum by several methods, composition of algorithms of the form $ \widehat{X} = \widehat{X} _ {2} ( \widehat{X} _ {1} ( \c
    13 KB (1,911 words) - 08:00, 6 June 2020
  • ...ve sequence of rational numbers is treated the same way. Schemes of normal algorithms can be uniquely coded by words over the alphabet $ \{ 0 , 1 \} $. ...r and equality, as well as the arithmetical operations (these are given by algorithms). The system of constructive real numbers with these order and equality rel
    20 KB (2,978 words) - 19:15, 18 January 2024
  • The idempotent correspondence principle is also valid for algorithms and their software and hardware implementations (cf. [[Idempotent algorithm
    4 KB (499 words) - 20:46, 16 November 2023
  • ...1]</TD> <TD valign="top"> J. Céa, "Lectures on optimization: theory and algorithms" , Springer (1978)</TD></TR><TR><TD valign="top">[12]</TD> <TD valign="top ...TD valign="top"> E.R. Edge, W.F. Powers, "Function-space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs" ''J.
    22 KB (3,158 words) - 19:38, 5 June 2020
  • .... Comprehensive introductions to quantum computation and the known quantum algorithms may be found in [[#References|[a2]]], [[#References|[a1]]]. ...quantum circuits) are preferred for describing and investigating specific algorithms. To obtain a quantum version of a classical model of deterministic computat
    15 KB (2,154 words) - 17:45, 1 July 2020
  • ...valign="top"> V.V. Voevodin, "Numerical methods of algebra. Theory and algorithms" , Moscow (1966) (In Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD
    4 KB (619 words) - 08:04, 6 June 2020
  • Convergence properties of stochastic approximation and other recursive algorithms have been the subject of much research. One approach is the "ordinary diff ...[a2]</TD> <TD valign="top"> L. Ljung, "Analysis of recursive stochastic algorithms" ''IEEE Trans. Autom. Control'' , '''AC-22''' (1977) pp. 551–575</TD><
    9 KB (1,349 words) - 08:23, 6 June 2020
  • There exist algorithms for the approximate construction of polynomials of best uniform approximati
    6 KB (907 words) - 08:06, 6 June 2020
  • ...etc.). A process has attributes (data structure) and a program of actions (algorithms). The model works on the principle of quasi-parallelism: at every moment on
    3 KB (533 words) - 17:14, 7 February 2011
  • ...><TR><TD valign="top">[21]</TD> <TD valign="top"> V.V. Ivanov, "Optimal algorithms for the numerical solution of singular integral equations" , ''Continuum Me
    20 KB (2,838 words) - 19:21, 13 January 2024
  • ...top">[a6]</TD> <TD valign="top"> J. O'Rourke, "Art gallery theorems and algorithms" , Oxford Univ. Press (1987)</TD></TR><TR><TD valign="top">[a7]</TD> <TD v
    3 KB (541 words) - 12:32, 27 August 2014
  • ...f an electrical circuit. Later [[Pattern recognition|pattern recognition]] algorithms were developed on the basis of tests. The test approach can be applied succ There is an abundance of algorithms for the construction of minimal tests. For example, for absolute tests by e
    22 KB (3,351 words) - 08:25, 6 June 2020
  • .../TR><TR><TD valign="top">[a5]</TD> <TD valign="top"> N.G. de Bruijn, "Some algorithms for ordering a sequence of objects, with application to E. Sparre Andersen'
    4 KB (549 words) - 18:47, 5 April 2020
  • ...as Toeplitz, Hankel, Vandermonde, Cauchy, and Pick matrices. Several fast algorithms have been devised over the years to exploit these special structures. Howev ...problems and the displacement theory gives new and efficient computational algorithms for solving a variety of such problems (see, e.g., [[#References|[a2]]] and
    21 KB (3,255 words) - 20:20, 13 January 2021
  • ..."top">[a10]</TD> <TD valign="top"> M. Gondran, M. Minoux, "Graphs and algorithms" , Wiley (1986) pp. Chapt. 5 (Translated from French)</TD></TR><TR><TD v
    10 KB (1,474 words) - 14:32, 7 June 2020
  • .... Bach, "Analytic methods in the analysis and design of number-theoretic algorithms" , MIT (1985)</TD></TR>
    3 KB (516 words) - 17:58, 8 November 2014
  • ...morphism between graphs is an important problem in graph theory. There are algorithms for certain classes of graphs with the aid of which isomorphism can be fair
    4 KB (648 words) - 17:28, 18 October 2014
  • ...<td valign="top"> H.G. Feichtinger, Th. Strohmer, "Gabor analysis and algorithms" , Birkhäuser (1998)</td></tr></table>
    4 KB (543 words) - 17:00, 1 July 2020
  • There exist algorithms by means of which it is possible to tell whether a language generated by so for which there are no algorithms by which it is possible to recognize, for arbitrary strings $ x $
    14 KB (2,055 words) - 07:50, 18 November 2023
  • ...3]</TD> <TD valign="top"> A.A. Markov, "On the impossibility of certain algorithms in the theory of associative systems" ''C.R. Acad. Sci. URSS'' , '''55'''
    9 KB (1,391 words) - 18:48, 5 April 2020
  • ...p"> D.E. Knuth, "The art of computer programming" , '''2: Seminumerical algorithms''' , Addison-Wesley (1998) (Edition: Third)</td></tr><tr><td valign="top"
    11 KB (1,706 words) - 18:55, 24 January 2024
  • ...za, "The acyclic orientation game on random graphs" ''Random Structures Algorithms'' , '''6''' (1995) pp. 261–268 (Proc. Sixth Internat. Sem. Random Grap
    10 KB (1,497 words) - 06:32, 26 March 2023
  • ...of inversion procedures, as well as the development of efficient numerical algorithms. In tomography a fundamental role is played by the [[Radon transform|Radon ==Reconstruction algorithms.==
    16 KB (2,342 words) - 17:25, 13 June 2020
  • is usually obtained on a computer by number-theoretic algorithms, of which the most widely used is the so-called method of residues, for exa ...cesses in technology, biology; etc. (see [[#References|[18]]]). Simulation algorithms are usually carefully developed; for example, they tabulate complicated fun
    24 KB (3,433 words) - 13:09, 13 January 2024
  • ...Salamin–Brent algorithm. There are also corresponding cubic, quartic, etc. algorithms, [[#References|[a2]]].
    4 KB (562 words) - 16:57, 1 July 2020
  • The collection of programs and program complexes by means of which: the algorithms in a program of a user, written in a high-level algorithmic language, are t ...fact, computer instructions, from the point of view of being able to write algorithms, are very elementary operations, and writing down an algorithm (programming
    19 KB (2,814 words) - 17:16, 7 February 2011
  • ...gorithmic approach to the Lovász local lemma, I" , ''Random Structures and Algorithms'' , '''2''' (1991) pp. 343–365 {{ZBL|0756.05080}}</TD></TR>
    4 KB (586 words) - 19:47, 18 December 2014
  • ...7]]] that this foundational system was inconsistent, the part dealing with algorithms only was isolated as the (type-free) lambda calculus. It turned out to be q terms can be used to represent algorithms, types serve to keep an order in these representing terms. (A similar role
    15 KB (2,306 words) - 16:57, 1 July 2020
  • <table><TR><TD valign="top">[1]</TD> <TD valign="top"> A.I. Mal'tsev, "Algorithms and recursive functions" , Wolters-Noordhoff (1970) (Translated from Russ
    5 KB (727 words) - 15:34, 4 March 2022
  • ...ies coincide. For channels with complete feedback, (en)coding and decoding algorithms have been proposed that are simple to describe and highly effective.
    5 KB (739 words) - 16:43, 4 June 2020
  • ...References|[a6]]]). Quick-sort is one of the most extensively investigated algorithms. To sort $n$ data items, it shows a quadratic worst-case and a $\Theta( n \ ...arge variation of behaviour has been observed for different satisfiability algorithms (for an overview, see [[#References|[a19]]]). For certain distributions the
    21 KB (3,198 words) - 18:47, 11 December 2020
  • ...td> <td valign="top"> N.J. Higham, "Accuracy and stability of numerical algorithms" , SIAM (Soc. Industrial Applied Math.) (1996)</td></tr></table>
    5 KB (740 words) - 17:44, 1 July 2020
  • ...8)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> H. Brent, "Algorithms for minimization without derivatives" , Prentice-Hall (1973)</TD></TR><TR>
    5 KB (774 words) - 17:33, 5 June 2020
  • ...sign. Stochastic programming methods can also be used to adapt systems and algorithms to random changes in the state of the medium in which they operate. Stochas
    5 KB (768 words) - 13:11, 3 May 2016
  • The use of adaptive algorithms is widespread. Often these methods are based on a way to estimate the error
    4 KB (650 words) - 15:07, 14 February 2020
  • Along with the methods described above, algorithms of another class, so called power methods, have been developed. The most ef ...ethods for solving positive-definite linear systems, and leads to the same algorithms: coordinate relaxation, sequential overrelaxation, steepest descent, and co
    19 KB (2,830 words) - 19:42, 27 February 2021
  • ...as benchmarks in the design, accuracy testing, and comparison of numerical algorithms. ...of PDEs into involutive form). Modern implementations of "triangulation" algorithms use a differential version of the [[Gröbner basis|Gröbner basis]] algorit
    23 KB (3,178 words) - 22:16, 5 June 2020
  • For recent (1998) surveys of algorithms for numerical linear algebra problems, see [[#References|[a2]]], [[#Referen ...usually FORTRAN, sometimes C or C++. Their main field of application is in algorithms with high numerical robustness and large scale computations.
    10 KB (1,478 words) - 17:02, 1 July 2020
  • ...to be an algorithm (a partial recursive function). By using an encoding of algorithms by numbers, one can write the condition "the number e is a realization of ...the logic of constructive mathematics" , ''Investigations on the theory of algorithms and mathematical logic'' , '''2''' , Moscow (1976) pp. 3–31 (In Russia
    12 KB (1,856 words) - 21:00, 4 June 2020
  • <table><TR><TD valign="top">[1]</TD> <TD valign="top"> R.P. Brent, "Algorithms for minimization without derivatives" , Prentice-Hall (1973)</TD></TR><TR>
    5 KB (766 words) - 08:12, 6 June 2020
  • ...e are many methods for obtaining such a sequence. However, the majority of algorithms suffer from a sharp deterioration when the level surfaces $ J ( x) = \tex ...References|[8]]]). For the case of minimization of a convex function these algorithms are very effective, since having a quadratic termination they do not requir
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  • Genetic algorithms, methods for finding maxima and minima of non-differentiable functions, dep
    4 KB (668 words) - 08:28, 6 June 2020
  • ...free semi-groups (see [[#References|[7]]]–[[#References|[9]]]). There are algorithms that recognize the solvability of arbitrary equations in a free semi-group.
    5 KB (786 words) - 20:17, 8 December 2015
  • ...TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> A.I. Mal'tsev, "Algorithms and recursive functions" , Wolters-Noordhoff (1970) (Translated from Russ
    6 KB (887 words) - 14:54, 7 June 2020
  • ...vergence bounds hold for conjugate gradient and related more sophisticated algorithms [[#References|[a4]]]. Even the basic Richardson method $ x _ {k + 1 } =
    5 KB (717 words) - 18:47, 5 April 2020
  • A number of minimization (reduction) algorithms and algorithms of automaton synthesis are associated with these methods of specifying auto Algorithms which yield the transition matrix of an automaton from formal schemes of th
    25 KB (3,544 words) - 07:31, 26 March 2023
  • ||{{Ref|Pr}}|| V. V. Prasolov, "Polynomials", vol. 11 of "Algorithms and Computation in Mathematics", Springer (2004).
    5 KB (801 words) - 20:34, 13 September 2016
  • ...al configurations, algorithms and their construction, optimization of such algorithms, as well as the solution of problems of enumeration, in particular the dete ...estigation is to elucidate the conditions for its existence and to develop algorithms for its construction.
    28 KB (4,167 words) - 17:45, 4 June 2020
  • ...top">[4]</TD> <TD valign="top"> Sh. Ushchumlich, "Investigation of some algorithms for the analysis and synthesis of automata" ''Soviet Math. Dokl.'' , '''20
    5 KB (830 words) - 14:27, 12 November 2023
  • ...parison of the experimental performance of several published approximation algorithms [[#References|[a3]]] indicates that the approach which best combines speed
    4 KB (704 words) - 12:30, 17 February 2021
  • ...ristic, LPT has become a touchstone for the design of heuristic scheduling algorithms of high quality.
    5 KB (739 words) - 16:43, 3 August 2014
  • ...D valign="top">[a2]</TD> <TD valign="top"> M.A.A. van Leeuwen, "Tableau algorithms defined naturally for pictures" ''Discrete Math.'' , '''157''' (1996) pp
    5 KB (742 words) - 08:06, 6 June 2020
  • de Casteljau algorithms using Bézier points $ \mathbf b _ {ij } $,
    6 KB (872 words) - 06:29, 30 May 2020
  • ...ces|[a3]]], [[#References|[a4]]], [[#References|[a2]]]. Projection pursuit algorithms approximate a function of $n$ variables by functions of the form
    5 KB (780 words) - 16:45, 1 July 2020
  • .../TD> <TD valign="top"> M. Minoux, "Mathematical programming: theory and algorithms" , Wiley (1986)</TD></TR> ...op">[7]</TD> <TD valign="top"> A.R.G. Heesterman, "Matrices and simplex algorithms" , Reidel (1983)</TD></TR>
    12 KB (2,034 words) - 09:14, 9 June 2016
  • In view of the wide use of systems of distinct representatives, algorithms for their practical determination (see [[#References|[1]]]) are of interest
    6 KB (900 words) - 08:25, 6 June 2020
  • ...</TD> <TD valign="top"> G.P. McCormick, "Nonlinear programming: theory, algorithms, and applications" , Wiley (1983)</TD></TR>
    5 KB (749 words) - 13:25, 3 May 2016
  • ...4]</TD> <TD valign="top"> J. Cea, "Lectures on optimization: theory and algorithms" , Springer (1978)</TD></TR></table>
    6 KB (879 words) - 19:35, 12 January 2024
  • A processing stage in computer vision algorithms, aimed at detecting and classifying the nature of junctions in the image do
    5 KB (686 words) - 16:45, 1 July 2020
  • Carlo (MCMC) algorithms are Markov chains, where at each iteration, depends on the current state. These stochastic algorithms are used
    16 KB (2,671 words) - 20:19, 12 March 2016
  • ...omplex data structures that are necessary for the effective realization of algorithms on a computer. The examples mentioned characterize fairly clearly the speci ...Algol-68|Algol-68]]) to the language of Post algorithms or Markov's normal algorithms. The deduction rules in this language (in their interaction with actual mea
    35 KB (5,424 words) - 11:17, 26 March 2023
  • ...has many applications in stability and control theory; efficient numerical algorithms for solving it are available.
    5 KB (876 words) - 16:52, 1 July 2020
  • ...lator" property of APL enables efficient debugging. The implementation of algorithms in APL, often just for the purpose of rapid prototyping, is typically very
    5 KB (736 words) - 18:47, 5 April 2020
  • ..."top"> C.H. Papadimitriou, K. Steiglitz, "Combinatorial optimization. Algorithms and complexity" , Prentice-Hall (1982) pp. 247ff</TD></TR><TR><TD valign=
    5 KB (752 words) - 08:29, 6 June 2020
  • ...theory of linear extrapolation and filtration, which yields optimal linear algorithms for the prediction and approximation of stochastic processes; this theory i
    6 KB (906 words) - 17:31, 5 June 2020
  • have Euclidean algorithms (cf. [[Euclidean algorithm|Euclidean algorithm]]) and the corresponding gro
    5 KB (775 words) - 07:59, 26 March 2023
  • ...nnected with the minimization of Boolean functions and the theory of local algorithms. These characteristics are the dimension and the extent of functions. ...shortest disjunctive normal form" are non-computable in the class of local algorithms.
    14 KB (2,056 words) - 06:28, 30 May 2020
  • ...ee [[#References|[a3]]] for a discussion of these results and of efficient algorithms for evaluating performance measures in the case of a closed network; a key
    5 KB (732 words) - 08:05, 6 June 2020
  • In two special cases there exist algorithms for calculating $ u _ {H} ( x) $
    7 KB (1,037 words) - 17:08, 13 January 2024
  • The matching polynomial was introduced in [[#References|[a1]]]. Basic algorithms for finding matching polynomials of arbitrary graphs, basic properties of t
    6 KB (1,005 words) - 20:14, 15 March 2023
  • ...bjective of the particular investigation, and the development of effective algorithms for the solution of the direct problems for these models. The development of effective algorithms for the solution of direct problems in geophysics rendered the interpretati
    13 KB (1,884 words) - 19:41, 5 June 2020
  • ...um information theory, quantum communication, quantum computation, quantum algorithms and their complexity, and quantum control. The science of quantum informati ...at simulating quantum mechanical systems resulted in exponentially complex algorithms compared to the physical resources associated with the system simulated. In
    21 KB (3,030 words) - 16:52, 1 July 2020
  • ...a (2004, 2010) for more detailed explanations, and Devroye (1986) for more algorithms. In what follows, $U$ is Uniform$(0,1)$ unless otherwise specified. ...}\frac{\alpha^\alpha}{a^a}e^{-(\alpha-a)}$. There are many other efficient algorithms.
    19 KB (2,851 words) - 07:04, 7 March 2024
  • ...limination of certain elementary conjunctions. Therefore many minimization algorithms employ the abridged disjunctive normal form as the initial specification of
    11 KB (1,546 words) - 06:28, 30 May 2020
  • ...[[#References|[a11]]], and the more general the AECM [[#References|[a23]]] algorithms build on the ECM algorithm by allowing this approximation to vary from CM-s ...nd stability of the EM algorithm. This results in simple, stable, and fast algorithms in a number of statistical applications. For example, in the $t$-model this
    26 KB (3,861 words) - 17:03, 1 July 2020
  • ...ng, elementary number theory, meta-mathematics, set theory, and concurrent algorithms. Recently (1998), NQTHM has been used to develop a machine-checked proof of
    5 KB (832 words) - 18:51, 24 March 2012
  • ...TD valign="top"> , ''Theoretical foundations and construction of numerical algorithms of problems of mathematical physics'' , Moscow (1979) (In Russian)</TD></
    7 KB (987 words) - 14:03, 24 December 2020
  • ...a1]</TD> <TD valign="top"> R.L. Adler, D. Coppersmith, M. Hassner, "Algorithms for sliding block codes" ''IEEE Trans. Inform. Theory'' , '''29''' (1983)
    6 KB (862 words) - 08:13, 6 June 2020
  • ...rogramming]] in general, is whether there exist polynomial-bounded (exact) algorithms for their solution. Until now (1991) this question is still open. ...enstra, A.H.G. Rinnooy Kan, D.B. Shmoys, "Sequencing and scheduling: algorithms and complexity" , ''Report BS-R8909'' , CWI (1989)</TD></TR><TR><TD valign
    13 KB (2,058 words) - 14:54, 7 June 2020
  • ...he general problem of synthesis of automata. There exist several heuristic algorithms for the synthesis of minimal schemes for automata, based on the special pro
    7 KB (1,011 words) - 18:49, 5 April 2020
  • ...ignal processing and systems theory. For such matrices there are different algorithms (N. Levison, I. Schur and others) for inversion. The inverse of a finite To
    6 KB (899 words) - 20:27, 17 January 2024
  • ...e constructed up to the end of the 1940-s. In the 1930-s, highly effective algorithms (as regards the number of arithmetic operations) were developed for calcula ...ration methods]] for a description of the QR algorithm and other iterative algorithms for calculating eigen values.
    15 KB (2,340 words) - 08:54, 21 January 2024
  • ...rcial microcontrollers, parts of commercial microprocessors, and their key algorithms have been verified mechanically, although the largest commercial chips are
    6 KB (814 words) - 19:26, 16 April 2014
  • ...e International Federation for Information Processing, for the exchange of algorithms, their effective realization by various computers, and as a means of their
    6 KB (897 words) - 20:29, 5 December 2023
  • ...tive algebra, polynomial ideal theory) can be reduced by structurally easy algorithms to the construction of Gröbner bases; and
    6 KB (1,000 words) - 17:05, 7 July 2014
  • ...y is based on keeping secret the nature of the enciphering and deciphering algorithms. Restricted cryptosystems are usually designed by amateurs and are almost a ...if its security lies not in the secrecy of the enciphering and deciphering algorithms, but rather in a relatively short secret parameter known as the key. It sho
    35 KB (5,528 words) - 19:33, 19 January 2024
  • ...is the study of the general properties of a coding and the construction of algorithms for recognizing these properties (see [[Coding, alphabetical|Coding, alphab ...investigations have been carried out of the possible encoding and decoding algorithms and upper bounds for the complexity of the encoder and decoder have been ob
    22 KB (3,518 words) - 08:18, 13 January 2024

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