A new method for computing the matrix exponential operation based on vector valued rational approximations
type: Item
instance of: scholarly article
title: A new method for computing the matrix exponential operation based on vector valued rational approximations
zbMATH Open document ID: 1242.65092
author: Xiaojing Zhu
author: Chuanqing Gu
author: Chunjing Li
published in: Journal of Computational and Applied Mathematics
publication date: 2012-03-19T00:00:00Z
review text: The authors propose a vector valued rational approximation method to compute a matrix exponential, \(e^{At}b\), where \(A\) is a complex matrix, \(t\) is a positive real number, and \(b\) is a vector. The proposed method is based on linear least-squares to evaluate the coefficients of the denominator polynomials, in which no matrix multiplications nor divisions are required. The proposed method is especially effective for fixed \(A\), \(b\), and many values of \(t\) due to a technique of scaling and recurrence. The authors also give an error analysis and numerical results.
Mathematics Subject Classification ID: 65F60
Mathematics Subject Classification ID: 15A16
zbMATH DE Number: 6015746
zbMATH Keywords: matrix exponential
zbMATH Keywords: vector-valued rational approximation
zbMATH Keywords: scaling
zbMATH Keywords: recurrence
describes a project that uses: MATLAB expm
describes a project that uses: mftoolbox
MaRDI profile type: Publication
full work available at URL: j.cam.2011.11.018
OpenAlex ID: W2026863659
cites work: Nineteen Dubious Ways to Compute the Exponential of a Matrix
cites work: Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
cites work: Functions of Matrices
cites work: Computing $A^\alpha, \log(A)$, and Related Matrix Functions by Contour Integrals
cites work: On Krylov Subspace Approximations to the Matrix Exponential Operator
cites work: Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
cites work: Rational approximations from power series of vector-valued meromorphic functions
cites work: Vector valued rational interpolants. I
cites work: Multivariate generalized inverse vector-valued rational interpolants
cites work: Vector valued Thiele-Werner-type osculatory rational interpolants.
cites work: Approximation of Matrix-Valued Functions
cites work: Q5689624
cites work: Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants
cites work: The Scaling and Squaring Method for the Matrix Exponential Revisited
cites work: A New Scaling and Squaring Algorithm for the Matrix Exponential
DOI: 10.1016/J.CAM.2011.11.018
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description: scientific article; zbMATH DE number 6015746