Padé approximation for the exponential of a block triangular matrix
type: Item
instance of: scholarly article
title: Padé approximation for the exponential of a block triangular matrix
zbMATH Open document ID: 0958.65050
DOI: 10.1016/S0024-3795(00)00042-2
author: Luca Dieci
author: Alessandra Papini
published in: Linear Algebra and its Applications
publication date: 2001-03-28T00:00:00Z
review text: The problem of computing the exponential of a block triangular matrix via Padé approximation techniques is examined, where the blocks themselves are not necessarily triangular. The main result in the paper gives improved error bounds, both absolute and relative, when the matrix is \(2 \times 2\) with well scaled diagonal blocks. This yields a new scaling and squaring technique for such matrices as well as its corresponding error analysis. The new strategy produces satisfactory approximations, mainly by avoiding the problem of overscaling. The extension of the results to block triangular matrices with more than two diagonal blocks appears to be a straightforward matter.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 1446351
zbMATH Keywords: matrix exponential
zbMATH Keywords: Padé approximation
zbMATH Keywords: scaling and squaring
zbMATH Keywords: error bounds
zbMATH Keywords: block triangular matrices
reviewed by: Juan Pedro Milaszewicz
MaRDI profile type: Publication
cites work: The Padé method for computing the matrix exponential
cites work: Numerical integration of ordinary differential equations on manifolds
cites work: Conditioning and Padé Approximation of the Logarithm of a Matrix
cites work: Padé approximations to the operator exponential
cites work: Q3359644
cites work: Q4000061
cites work: Perturbation theory and backward error for \(AX - XB = C\)
cites work: On Krylov Subspace Approximations to the Matrix Exponential Operator
cites work: Exponential Integrators for Large Systems of Differential Equations
cites work: Bounds and perturbation bounds for the matrix exponential
cites work: Padé error estimates for the logarithm of a matrix
cites work: A Schur--Fréchet Algorithm for Computing the Logarithm and Exponential of a Matrix
cites work: The Sensitivity of the Matrix Exponential
cites work: Nineteen Dubious Ways to Compute the Exponential of a Matrix
cites work: Numerical Computation of the Matrix Exponential with Accuracy Estimate
description: scientific article; zbMATH DE number 1446351