The Leja Method Revisited: Backward Error Analysis for the Matrix Exponential

DOI10.1137/15M1027620zbMath1339.65061arXiv1506.08665MaRDI QIDQ2811992

Peter Kandolf, Alexander Ostermann, Stefan Rainer, Marco Caliari

Publication date: 10 June 2016

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.08665

zbMATH Keywords

numerical exampleTaylor seriesbackward error analysispolynomial interpolationexponential integratorsaction of matrix exponentialLeja interpolation\(\varphi\) functions

Mathematics Subject Classification ID

Numerical interpolation (65D05) Numerical computation of matrix exponential and similar matrix functions (65F60)

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Uses Software

• Expokit
• Matlab
• SparseMatrix
• mctoolbox
• Eigtool
• Algorithm 919
• phipm

Cites Work

• Unnamed Item
• Newton interpolation at Leja points
• Interpolating discrete advection--diffusion propagators at Leja sequences
• A residual based error estimate for Leja interpolation of matrix functions
• Comparison of software for computing the action of the matrix exponential
• Accurate evaluation of divided differences for polynomial interpolation of exponential propagators
• Exponential integrators
• The university of Florida sparse matrix collection
• Algorithm 919
• Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
• Error Analysis of Direct Methods of Matrix Inversion
• Expokit
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• Meshfree Exponential Integrators
• Functions of Matrices

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