Double-shift-invert Arnoldi method for computing the matrix exponential

DOI10.1007/s13160-018-0309-9zbMath1447.65008OpenAlexW2800691151WikidataQ115601123 ScholiaQ115601123MaRDI QIDQ1756729

Takashi Nodera, Yuka Hashimoto

Publication date: 21 December 2018

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13160-018-0309-9

zbMATH Keywords

matrix exponentialevolution differential equationdouble shift Arnoldi

Mathematics Subject Classification ID

Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22) Numerical computation of matrix exponential and similar matrix functions (65F60)

Uses Software

• MATLAB expm

Cites Work

• Rational Krylov sequence methods for eigenvalue computation
• Approximation of exp(-x) by rational functions with concentrated negative poles
• Numerical ranges and stability estimates
• RD-rational approximations of the matrix exponential
• Error Estimates and Evaluation of Matrix Functions via the Faber Transform
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Efficient Solution of Parabolic Equations by Krylov Approximation Methods
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• The Reaction-Diffusion Master Equation as an Asymptotic Approximation of Diffusion to a Small Target
• Uniform Approximation of $\varphi$-Functions in Exponential Integrators by a Rational Krylov Subspace Method with Simple Poles
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• Parallelization of the Rational Arnoldi Algorithm
• Preconditioning Lanczos Approximations to the Matrix Exponential

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