Journal Article

Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators

Al-Mohy, Awad H., Higham, Nicholas J.

2011

Overview

A new algorithm is developed for computing ..., where A is an n x n matrix and B is ... with ... The algorithm works for any A, its computational cost is dominated by the formation of products of A with ... matrices, and the only input parameter is a backward error tolerance. The algorithm can return a single matrix ... or a sequence ... on an equally spaced grid of points ... It uses the scaling part of the scaling and squaring method together with a truncated Taylor series approximation to the exponential. Numerical experiments show that the algorithm performs in a numerically stable fashion across a wide range of problems, and analysis of rounding errors and of the conditioning of the problem provides theoretical support. Experimental comparisons with MATLAB codes based on Krylov subspace, Chebyshev polynomial, and Laguerre polynomial methods show the new algorithm to be sometimes much superior in terms of computational cost and accuracy.(ProQuest: ... denotes formulae/symbols omitted.)

• Publisher: Society for Industrial and Applied Mathematics
• Subject: Algebra / Algorithms / Computation / Computational efficiency / Error analysis / Exact sciences and technology / Linear and multilinear algebra, matrix theory / Mathematical analysis / Mathematical models / Mathematics / Matlab / Matrices / Matrix / Methods of scientific computing (including symbolic computation, algebraic computation) / Numerical analysis / Numerical analysis. Scientific computation / Numerical linear algebra / Sciences and techniques of general use / Studies / Taylor series