On the backward and forward error of approximations of analytic functions and applications to the computation of matrix functions

DOI10.1016/j.cam.2022.114706zbMath1502.65022OpenAlexW4292263693WikidataQ113878678 ScholiaQ113878678MaRDI QIDQ2088843

Jorge Sastre, Jacinto-Javier Ibáñez

Publication date: 6 October 2022

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.2022.114706

zbMATH Keywords

Padé approximationTaylor seriesmatrix functionsfunction approximationbackward errorforward error

Mathematics Subject Classification ID

Approximation by polynomials (41A10) Algorithms for approximation of functions (65D15) Matrix exponential and similar functions of matrices (15A16) Real rational functions (26C15) Numerical computation of matrix exponential and similar matrix functions (65F60) Software, source code, etc. for problems pertaining to approximations and expansions (41-04)

Related Items (1)

Euler polynomials for the matrix exponential approximation

Uses Software

• LAPACK
• mctoolbox
• testmatrix
• MATLAB expm
• mftoolbox
• SONEST
• CONEST

Cites Work

• Unnamed Item
• Accurate matrix exponential computation to solve coupled differential models in engineering
• Efficient orthogonal matrix polynomial based method for computing matrix exponential
• Rational approximations of trigonometric matrices with application to second-order systems of differential equations
• On-the-fly backward error estimate for matrix exponential approximation by Taylor algorithm
• Efficient evaluation of matrix polynomials
• Two algorithms for computing the matrix cosine function
• Boosting the computation of the matrix exponential
• Fast Taylor polynomial evaluation for the computation of the matrix cosine
• Efficient computation of the matrix cosine
• Efficient algorithms for the matrix cosine and sine
• Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm
• Approximate Diagonalization
• A New Scaling and Squaring Algorithm for the Matrix Exponential
• FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation
• Computing the Wave-Kernel Matrix Functions
• Accuracy and Stability of Numerical Algorithms
• New Scaling-Squaring Taylor Algorithms for Computing the Matrix Exponential
• New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• Functions of Matrices
• On the Number of Nonscalar Multiplications Necessary to Evaluate Polynomials

This page was built for publication: On the backward and forward error of approximations of analytic functions and applications to the computation of matrix functions