Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation

Philipp Bader, Sergio Blanes and Fernando Casas
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Philipp Bader: Departament de Matemàtiques, Universitat Jaume I, 12071 Castellón, Spain
Sergio Blanes: Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 Valencia, Spain
Fernando Casas: IMAC and Departament de Matemàtiques, Universitat Jaume I, 12071 Castellón, Spain

Mathematics, 2019, vol. 7, issue 12, 1-19

Abstract: A new way to compute the Taylor polynomial of a matrix exponential is presented which reduces the number of matrix multiplications in comparison with the de-facto standard Paterson-Stockmeyer method for polynomial evaluation. Combined with the scaling and squaring procedure, this reduction is sufficient to make the Taylor method superior in performance to Padé approximants over a range of values of the matrix norms. An efficient adjustment to make the method robust against overscaling is also introduced. Numerical experiments show the superior performance of our method to have a similar accuracy in comparison with state-of-the-art implementations, and thus, it is especially recommended to be used in conjunction with Lie-group and exponential integrators where preservation of geometric properties is at issue.

Keywords: exponential of a matrix; scaling and squaring; matrix polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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