RD-rational approximations of the matrix exponential
type: Item
instance of: scholarly article
title: RD-rational approximations of the matrix exponential
zbMATH Open document ID: 1075.65062
published in: BIT
publication date: 2005-04-07T00:00:00Z
review text: Given a square matrix \(A\) and a vector \(v\), the authors propose two methods for approximating the function \(\exp(-tA) v\). Both methods are based on the Krylov subspace of the matrix \(Z = (I+hA)^{-1}\) applied to \(v\) for some fixed parameter \(h\). If \(V\) denotes an orthonormal basis of this Krylov subspace then the first method (called Arnoldi RD-method) uses the approximation \(V \exp(-\frac t h (H^{-1}-I)) V^T v\), where \(H = V^T A V\). This is shown to be closely related with the polynomial interpolation of the function \(f(z) = \exp(-\frac t h (1/z-1))\) in the eigenvalues of \(H\). The other method (called Arnoldi RF-method) is obtained by using the zeros of Faber polynomials as interpolation points. Some error bounds are provided and numerical experiments compare the two methods with other existing methods for approximating \(\exp(-tA) v\), such as the classical Krylov subspace method and Padé approximations.
reviewed by: Daniel Kressner
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 2153696
zbMATH Keywords: Krylov subspace methods
zbMATH Keywords: matrix exponential
zbMATH Keywords: rational approximation
zbMATH Keywords: comparison of methods
zbMATH Keywords: Arnoldi RD-method
zbMATH Keywords: Arnoldi RF-method
zbMATH Keywords: Faber polynomials
zbMATH Keywords: error bounds
zbMATH Keywords: numerical experiments
zbMATH Keywords: Padé approximations
author: Igor Moret
author: P. Novati
describes a project that uses: MATLAB ODE suite
MaRDI profile type: Publication
full work available at URL: b:bitn.0000046805.27551.3b
OpenAlex ID: W2092112892
DOI: 10.1023/B:BITN.0000046805.27551.3B
description: scientific article; zbMATH DE number 2153696