Impact of accuracy optimization on the convergence of numerical iterative methods

Nasrine Damouche; Matthieu Martel; Alexandre Chapoutot

doi:10.1007/978-3-319-27436-2_9

Impact of accuracy optimization on the convergence of numerical iterative methods

Nasrine Damouche, Matthieu Martel, Alexandre Chapoutot

Université de Perpignan

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Among other objectives, rewriting programs serves as a useful technique to improve numerical accuracy. However, this optimization is not intuitive and this is why we switch to automatic transformation techniques. We are interested in the optimization of numerical programs relying on the IEEE754 floating-point arithmetic. In this article, our main contribution is to study the impact of optimizing the numerical accuracy of programs on the time required by numerical iterative methods to converge. To emphasize the usefulness of our tool, we make it optimize several examples of numerical methods such as Jacobi’s method, Newton-Raphson’s method, etc. We show that significant speedups are obtained in terms of number of iterations, time and flops.

Original language	English
Title of host publication	Logic-Based Program Synthesis and Transformation - 25th International Symposium, LOPSTR 2015, Revised Selected Papers
Editors	Moreno Falaschi
Publisher	Springer Verlag
Pages	143-160
Number of pages	18
ISBN (Print)	9783319274355
DOIs	https://doi.org/10.1007/978-3-319-27436-2_9
Publication status	Published - 1 Jan 2015
Event	25th International Symposium on Logic-Based Program Synthesis and Transformation, LOPSTR 2015 - Siena, Italy Duration: 13 Jul 2015 → 15 Jul 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9527
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	25th International Symposium on Logic-Based Program Synthesis and Transformation, LOPSTR 2015
Country/Territory	Italy
City	Siena
Period	13/07/15 → 15/07/15

Keywords

Convergence acceleration
Floating-point numbers
IEEE754 standard
Numerical analysis
Program transformation

Access to Document

10.1007/978-3-319-27436-2_9

Cite this

Damouche, N., Martel, M., & Chapoutot, A. (2015). Impact of accuracy optimization on the convergence of numerical iterative methods. In M. Falaschi (Ed.), Logic-Based Program Synthesis and Transformation - 25th International Symposium, LOPSTR 2015, Revised Selected Papers (pp. 143-160). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9527). Springer Verlag. https://doi.org/10.1007/978-3-319-27436-2_9

Damouche, Nasrine ; Martel, Matthieu ; Chapoutot, Alexandre. / Impact of accuracy optimization on the convergence of numerical iterative methods. Logic-Based Program Synthesis and Transformation - 25th International Symposium, LOPSTR 2015, Revised Selected Papers. editor / Moreno Falaschi. Springer Verlag, 2015. pp. 143-160 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Impact of accuracy optimization on the convergence of numerical iterative methods",

abstract = "Among other objectives, rewriting programs serves as a useful technique to improve numerical accuracy. However, this optimization is not intuitive and this is why we switch to automatic transformation techniques. We are interested in the optimization of numerical programs relying on the IEEE754 floating-point arithmetic. In this article, our main contribution is to study the impact of optimizing the numerical accuracy of programs on the time required by numerical iterative methods to converge. To emphasize the usefulness of our tool, we make it optimize several examples of numerical methods such as Jacobi{\textquoteright}s method, Newton-Raphson{\textquoteright}s method, etc. We show that significant speedups are obtained in terms of number of iterations, time and flops.",

keywords = "Convergence acceleration, Floating-point numbers, IEEE754 standard, Numerical analysis, Program transformation",

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Damouche, N, Martel, M & Chapoutot, A 2015, Impact of accuracy optimization on the convergence of numerical iterative methods. in M Falaschi (ed.), Logic-Based Program Synthesis and Transformation - 25th International Symposium, LOPSTR 2015, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9527, Springer Verlag, pp. 143-160, 25th International Symposium on Logic-Based Program Synthesis and Transformation, LOPSTR 2015, Siena, Italy, 13/07/15. https://doi.org/10.1007/978-3-319-27436-2_9

Impact of accuracy optimization on the convergence of numerical iterative methods. / Damouche, Nasrine; Martel, Matthieu; Chapoutot, Alexandre.
Logic-Based Program Synthesis and Transformation - 25th International Symposium, LOPSTR 2015, Revised Selected Papers. ed. / Moreno Falaschi. Springer Verlag, 2015. p. 143-160 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9527).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Martel, Matthieu

AU - Chapoutot, Alexandre

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2015.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Among other objectives, rewriting programs serves as a useful technique to improve numerical accuracy. However, this optimization is not intuitive and this is why we switch to automatic transformation techniques. We are interested in the optimization of numerical programs relying on the IEEE754 floating-point arithmetic. In this article, our main contribution is to study the impact of optimizing the numerical accuracy of programs on the time required by numerical iterative methods to converge. To emphasize the usefulness of our tool, we make it optimize several examples of numerical methods such as Jacobi’s method, Newton-Raphson’s method, etc. We show that significant speedups are obtained in terms of number of iterations, time and flops.

AB - Among other objectives, rewriting programs serves as a useful technique to improve numerical accuracy. However, this optimization is not intuitive and this is why we switch to automatic transformation techniques. We are interested in the optimization of numerical programs relying on the IEEE754 floating-point arithmetic. In this article, our main contribution is to study the impact of optimizing the numerical accuracy of programs on the time required by numerical iterative methods to converge. To emphasize the usefulness of our tool, we make it optimize several examples of numerical methods such as Jacobi’s method, Newton-Raphson’s method, etc. We show that significant speedups are obtained in terms of number of iterations, time and flops.

KW - Convergence acceleration

KW - Floating-point numbers

KW - IEEE754 standard

KW - Numerical analysis

KW - Program transformation

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Logic-Based Program Synthesis and Transformation - 25th International Symposium, LOPSTR 2015, Revised Selected Papers

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Damouche N, Martel M, Chapoutot A. Impact of accuracy optimization on the convergence of numerical iterative methods. In Falaschi M, editor, Logic-Based Program Synthesis and Transformation - 25th International Symposium, LOPSTR 2015, Revised Selected Papers. Springer Verlag. 2015. p. 143-160. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-27436-2_9

Impact of accuracy optimization on the convergence of numerical iterative methods

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