alexa Stability of the Generalized Polar Decomposition Method for the Approximation of the Matrix Exponential | OMICS International | Abstract
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
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Research Article

Stability of the Generalized Polar Decomposition Method for the Approximation of the Matrix Exponential

Elham Nobari and S. Mohammad Hosseini*

Department of Mathematics, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran

Corresponding Author:
S. Mohammad Hosseini
Department of Mathematics
Tarbiat Modares University
P.O. Box 14115-175, Tehran, Iran
Email: hossei [email protected]

Received date: 01 September 2009; Revised date: 03 September 2010; Accepted date: 05 September 2010

Abstract

Generalized polar decomposition method (or briefly GPD method) has been introduced by Munthe-Kaas and Zanna [5] 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 ∈ g, a Lie algebra of matrices and computing exp(Z)v for a vector 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 v.

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