Parallel matrix function evaluation via initial value ODE modeling

International audienceThe 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