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Toward Abstract Numerical Analysis

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Webb MillerAuthors Info & Claims

Journal of the ACM (JACM), Volume 20, Issue 3

Pages 399 - 408

https://doi.org/10.1145/321765.321772

Published: 01 July 1973 Publication History

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Abstract

This paper deals with a technique for proving that certain problems of numerical analysis are numerically unsolvable. So that only methods which are natural for dealing with analytic problems may be presented, notions from recursive function theory have been avoided. Instead, the number of necessary function evaluations is taken as the measure of computational complexity. The role of topological concepts in the study of computability is examined. Last, a topological result is used to prove that a simple initial-value problem is numerically unsolvable.

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Havránek T(2005)The approximation problem in computational statisticsMathematical Foundations of Computer Science 1975 4th Symposium, Mariánské Lázně, September 1–5, 197510.1007/3-540-07389-2_205(258-265)Online publication date: 21-May-2005
https://doi.org/10.1007/3-540-07389-2_205
Ko K(1982)The maximum value problem and NP real numbersJournal of Computer and System Sciences10.1016/0022-0000(82)90053-824:1(15-35)Online publication date: Feb-1982
https://doi.org/10.1016/0022-0000(82)90053-8
Meersman R(1975)A survey of techniques in applied computational complexityJournal of Computational and Applied Mathematics10.1016/0771-050X(75)90005-41:1(39-46)Online publication date: Mar-1975
https://doi.org/10.1016/0771-050X(75)90005-4

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Toward Abstract Numerical Analysis

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Published In

Journal of the ACM Volume 20, Issue 3

July 1973

175 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321765

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 1973

Published in JACM Volume 20, Issue 3

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Havránek T(2005)The approximation problem in computational statisticsMathematical Foundations of Computer Science 1975 4th Symposium, Mariánské Lázně, September 1–5, 197510.1007/3-540-07389-2_205(258-265)Online publication date: 21-May-2005
https://doi.org/10.1007/3-540-07389-2_205
Ko K(1982)The maximum value problem and NP real numbersJournal of Computer and System Sciences10.1016/0022-0000(82)90053-824:1(15-35)Online publication date: Feb-1982
https://doi.org/10.1016/0022-0000(82)90053-8
Meersman R(1975)A survey of techniques in applied computational complexityJournal of Computational and Applied Mathematics10.1016/0771-050X(75)90005-41:1(39-46)Online publication date: Mar-1975
https://doi.org/10.1016/0771-050X(75)90005-4

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Error analysis of the numerical solution of split differential equations

Numerical stability analysis of the pseudo-spectral analytical time-domain PIC algorithm

Toward Non Commutative Numerical Analysis: High Order Integration in Time

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