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2011 Stability of the Generalized Polar Decomposition Method for the Approximation of the Matrix Exponential
Mohammad Hosseini, Elham Nobari
J. Gen. Lie Theory Appl. 5: 1-12 (2011). DOI: 10.4303/jglta/G090901

Abstract

Generalized polar decomposition method (or briefly GPD method) has been introduced by Munthe-Kaas and Zanna to approximate the matrix exponential. In this paper, we investigate the numerical stability of that method with respect to roundoff propagation. The numerical GPD method includes two parts: splitting of a matrix $Z\in \mathfrak{g}$, a Lie algebra of matrices and computing $\exp(Z)\mathbf{v}$ for a vector $\mathbf{v}$. We show that the former is stable provided that $\|Z\|$ is not so large, while the latter is not stable in general except with some restrictions on the entries of the matrix Z and the vector $\mathbf{v}$.

Citation

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Mohammad Hosseini. Elham Nobari. "Stability of the Generalized Polar Decomposition Method for the Approximation of the Matrix Exponential." J. Gen. Lie Theory Appl. 5 1 - 12, 2011. https://doi.org/10.4303/jglta/G090901

Information

Published: 2011
First available in Project Euclid: 29 September 2011

zbMATH: 1216.65052
MathSciNet: MR2795577
Digital Object Identifier: 10.4303/jglta/G090901

Subjects:
Primary: 65F30, 65G5, 65L07

Rights: Copyright © 2011 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

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