TY - GEN
T1 - Impact of accuracy optimization on the convergence of numerical iterative methods
AU - Damouche, Nasrine
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
UR - https://www.scopus.com/pages/publications/84952801972
U2 - 10.1007/978-3-319-27436-2_9
DO - 10.1007/978-3-319-27436-2_9
M3 - Conference contribution
AN - SCOPUS:84952801972
SN - 9783319274355
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 143
EP - 160
BT - Logic-Based Program Synthesis and Transformation - 25th International Symposium, LOPSTR 2015, Revised Selected Papers
A2 - Falaschi, Moreno
PB - Springer Verlag
T2 - 25th International Symposium on Logic-Based Program Synthesis and Transformation, LOPSTR 2015
Y2 - 13 July 2015 through 15 July 2015
ER -