Parallel matrix function evaluation via initial value ODE modeling

Jean-Paul Chehab (1) , Madalina Petcu

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

The purpose of this article is to propose ODE based approaches for the numerical evaluation of matrix functions f (A), a question of major interest in the numerical linear algebra. For that, we model f (A) as the solution at a finite time T of a time dependent equation. We use parallel algorithms, such as the parareal method, on the time interval [0, T] in order to solve the obtained evolution equation. When f (A) is reached as a stable steady state, it can be computed by combining parareal algorithms and optimal control techniques. Numerical illustrations are given. (C) 2016 Elsevier Ltd. All rights reserved.

Domaines: Mathématiques [math]

Jean-Paul Chehab, Madalina Petcu. Parallel matrix function evaluation via initial value ODE modeling. Computers & Mathematics with Applications, 2016, 72 (1), pp.76-91. ⟨10.1016/j.camwa.2016.04.036⟩. ⟨hal-03621854⟩