On-the-fly backward error estimate for matrix exponential approximation by Taylor algorithm

DOI10.1016/j.cam.2018.07.042zbMath1452.65082OpenAlexW2886775180WikidataQ115581059 ScholiaQ115581059MaRDI QIDQ1624675

Marco Caliari, Franco Zivcovich

Publication date: 16 November 2018

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

Full work available at URL: https://doi.org/10.1016/j.cam.2018.07.042

zbMATH Keywords

Krylov methodstruncated Taylor seriesscaling and squaring algorithmbackward error estimate for the matrix exponentialmultiple precision floating point computationoverscaling

Mathematics Subject Classification ID

Matrix exponential and similar functions of matrices (15A16) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (14)

A \(\mu\)-mode integrator for solving evolution equations in Kronecker form ⋮ Method for calculating multiwave scattering by layered anisotropic media ⋮ Efficient and accurate computation for the \(\varphi\)-functions arising from exponential integrators ⋮ Optimality of the Paterson-Stockmeyer method for evaluating matrix polynomials and rational matrix functions ⋮ Euler polynomials for the matrix exponential approximation ⋮ A second order directional split exponential integrator for systems of advection-diffusion-reaction equations ⋮ A \(\mu\)-mode BLAS approach for multidimensional tensor-structured problems ⋮ Jordan-Schur algorithms for computing the matrix exponential ⋮ A Fast Time Splitting Finite Difference Approach to Gross–Pitaevskii Equations ⋮ An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix Exponential ⋮ Computing the Lyapunov operator \(\varphi \)-functions, with an application to matrix-valued exponential integrators ⋮ On the backward and forward error of approximations of analytic functions and applications to the computation of matrix functions ⋮ Arbitrary Precision Algorithms for Computing the Matrix Cosine and its Fréchet Derivative ⋮ BAMPHI: matrix-free and transpose-free action of linear combinations of \(\varphi\)-functions from exponential integrators

Uses Software

• Matlab
• mctoolbox
• MATLAB expm

Cites Work

• Accurate matrix exponential computation to solve coupled differential models in engineering
• High performance computing of the matrix exponential
• Efficient orthogonal matrix polynomial based method for computing matrix exponential
• Backward error analysis of polynomial approximations for computing the action of the matrix exponential
• On the algorithm by Al-Mohy and Higham for computing the action of the matrix exponential: a posteriori roundoff error estimation
• The Leja Method Revisited: Backward Error Analysis for the Matrix Exponential
• Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators
• A New Scaling and Squaring Algorithm for the Matrix Exponential
• Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
• A note on the evaluation of matrix polynomials
• A Schur--Fréchet Algorithm for Computing the Logarithm and Exponential of a Matrix
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra
• Accurate and efficient matrix exponential computation
• Accurate Computation of Divided Differences of the Exponential Function
• New Scaling-Squaring Taylor Algorithms for Computing the Matrix Exponential
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• Functions of Matrices

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