Error analysis of two algorithms for the computation of the matrix exponential
type: Item
instance of: scholarly article
title: Error analysis of two algorithms for the computation of the matrix exponential
zbMATH Open document ID: 0778.65033
DOI: 10.1007/BF02576760
author: C. Fassino
author: Bruno Codenotti
published in: Calcolo
publication date: 1993-05-24T00:00:00Z
review text: This paper investigates the roundoff and truncation errors for the Taylor series of a matrix exponential. If the norm of the matrix \(A\) is less than one, the roundoff error grows linearly with respect to its size and norm; otherwise it grows exponentially. Hence for \(A\) with \(\| A\|\geq 1\) a scaling and squaring algorithm is introduced for \(m^{-1}A\) where \(m\) is a sufficiently large integer to give \(\| m^{-1}A\| < 1\): Compute the truncated Taylor series of \(m^{-1}A\) and raise it to the \(m\)-th power, where for ease of computations, \(m\) is chosen as a power of two. In the final analysis, the scaling and squaring algorithm is shown to be stable for all \(A\).
reviewed by: Frank Uhlig
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 165189
zbMATH Keywords: matrix exponential
zbMATH Keywords: roundoff error
zbMATH Keywords: scaling and squaring algorithm
zbMATH Keywords: truncated Taylor series
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 165189