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  • ...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.
    15 KB (2,349 words) - 09:05, 21 January 2024
  • ...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>
    7 KB (1,026 words) - 20:42, 16 November 2023
  • 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

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