International Symposium on Logic-Based Program Synthesis and Transformation

Logic-Based Program Synthesis and Transformation pp 143-160 | Cite as

Impact of Accuracy Optimization on the Convergence of Numerical Iterative Methods

  • Nasrine Damouche
  • Matthieu Martel
  • Alexandre Chapoutot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9527)

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.

Keywords

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

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Nasrine Damouche
    • 1
  • Matthieu Martel
    • 1
  • Alexandre Chapoutot
    • 2
  1. 1.University of Perpignan Via DomitiaLAMPSFrance
  2. 2.ENSTA ParisTechPalaiseauFrance

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