A self-validating numerical method for the matrix exponential
type: Item
instance of: scholarly article
title: A self-validating numerical method for the matrix exponential
zbMATH Open document ID: 0685.65035
DOI: 10.1007/BF02243806
published in: Computing
publication date: 1989-01-01T00:00:00Z
review text: An algorithm is presented which produces highly accurate and automatically verified bounds for \(\exp (A)=\sum^{\infty}_{k=0}A^ k/k!\) where A is a real \(n\times n\) matrix. The method is based on interval analysis techniques and the iterative defect correction principle. The ``scaling and squaring'' approach is realized by the Padé approximations and safe error monitoring. Finally there are three examples \((n=2\), \(n=3)\) in order to compare the numerical results with the results by conventional floating-point computations.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 4123165
zbMATH Keywords: matrix exponential
zbMATH Keywords: comparison of methods
zbMATH Keywords: interval analysis
zbMATH Keywords: iterative defect correction
zbMATH Keywords: scaling and squaring
zbMATH Keywords: Padé approximations
zbMATH Keywords: safe error monitoring
author: Pavel B. Bochev
author: Svetoslav Markov
describes a project that uses: HIFICOMP
MaRDI profile type: Publication
cites work: Accurate arithmetic results for decimal data on non-decimal computers
cites work: Q3948528
cites work: Nineteen Dubious Ways to Compute the Exponential of a Matrix
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cites work: Numerical Computation of the Matrix Exponential with Accuracy Estimate
description: scientific article; zbMATH DE number 4123165