Computing exponentials of essentially non-negative matrices entrywise to high relative accuracy

DOI10.1090/S0025-5718-2013-02677-4zbMath1279.65051OpenAlexW2092918057MaRDI QIDQ2840622

Jungong Xue, Qiang Ye

Publication date: 23 July 2013

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2013-02677-4

zbMATH Keywords

algorithmnumerical exampleserror analysisTaylor series methodmatrix exponentialspolynomial methodnon-negative matrices

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Numerical computation of matrix norms, conditioning, scaling (65F35) Conditioning of matrices (15A12) Matrix exponential and similar functions of matrices (15A16) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (4)

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Uses Software

• Expokit
• MATLAB expm
• mftoolbox

Cites Work

• Communicability graph and community structures in complex networks
• Entrywise relative perturbation bounds for exponentials of essentially non-negative matrices
• Quadrature rule-based bounds for functions of adjacency matrices
• Error analysis of two algorithms for the computation of the matrix exponential
• Bounds for the entries of matrix functions with applications to preconditioning
• Derivatives of the matrix exponential and their computation
• The Padé method for computing the matrix exponential
• Padé approximation for the exponential of a block triangular matrix
• Accurate computation of the smallest eigenvalue of a diagonally dominant $M$-matrix
• The Randomization Technique as a Modeling Tool and Solution Procedure for Transient Markov Processes
• A New Scaling and Squaring Algorithm for the Matrix Exponential
• Numerical Computation of the Matrix Exponential with Accuracy Estimate
• The Sensitivity of the Matrix Exponential
• Nineteen Dubious Ways to Compute the Exponential of a Matrix
• Expokit
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• Collective dynamics of ‘small-world’ networks
• Functions of Matrices
• Unnamed Item
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