Comparison of software for computing the action of the matrix exponential
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The implementation of exponential integrators requires the action of the matrix exponential and related functions of a possibly large matrix. There are various methods in the literature for carrying out this task. In this paper we describe a new implementation of a method based on interpolation at Leja points. We numerically compare this method with other codes from the literature. As we are interested in applications to exponential integrators we choose the test examples from spatial discretization of time dependent partial differential equations in two and three space dimensions. The test matrices thus have large eigenvalues and can be nonnormal.
KeywordsLeja interpolation Action of matrix exponential Krylov subspace method Taylor series Exponential integrators
Mathematics Subject Classification (2010)65F60 65D05 65L04