Impact of Accuracy Optimization on the Convergence of Numerical Iterative Methods

Nasrine Damouche (1) , Matthieu Martel (1) , Alexandre Chapoutot (2)

1 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations
2 SFL - Sûreté et Fiabilité des Logiciels

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.

Mots clés: Program Transformation; Floating-Point Numbers; IEEE754 Standard; Numerical analysis; Convergence acceleration

Domaines: Langage de programmation [cs.PL]

Nasrine Damouche, Matthieu Martel, Alexandre Chapoutot. Impact of Accuracy Optimization on the Convergence of Numerical Iterative Methods. Logic-Based Program Synthesis and Transformation, 9527, Springer Verlag, pp.143-160, 2015, Lecture Notes in Computer Science, 978-3-319-27435-5. ⟨10.1007/978-3-319-27436-2_9⟩. ⟨hal-01272514⟩