...(ed.) ''The Schur complement and its applications'', Numerical Methods and Algorithms '''4''' Springer (2005) {{ISBN|0-387-24271-6}} {{ZBL|1075.15002}}
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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>
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...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
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* Ivan Rival (ed.),"Algorithms and Order", Kluwer (1989) {{ISBN|940107691X}} {{ZBL|0709.68004}}
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...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)
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Some authors make a specific distinction between algorithms and procedures. Algorithms are prescriptions of sequences of actions which should always terminate aft
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...~/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
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...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