Entrywise relative perturbation bounds for exponentials of essentially non-negative matrices

DOI10.1007/s00211-008-0167-5zbMath1163.65021OpenAlexW2020051491MaRDI QIDQ958156

Qiang Ye, Jungong Xue

Publication date: 2 December 2008

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-008-0167-5

zbMATH Keywords

spectral radiuscondition numbermatrix exponentialsperturbation boundscontinuous-time Markov chainessentially non-negative matrices

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Continuous-time Markov processes on general state spaces (60J25) Inequalities involving eigenvalues and eigenvectors (15A42) Numerical analysis or methods applied to Markov chains (65C40) Matrices over function rings in one or more variables (15A54) Conditioning of matrices (15A12)

Related Items

Computing the exponential of large block-triangular block-Toeplitz matrices encountered in fluid queues, Computing exponentials of essentially non-negative matrices entrywise to high relative accuracy, Componentwise accurate fluid queue computations using doubling algorithms

Uses Software

• Expokit
• MATLAB expm

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bounds for the entries of matrix functions with applications to preconditioning
• Derivatives of the matrix exponential and their computation
• Padé approximation for the exponential of a block triangular matrix
• Approximation of Matrix-Valued Functions
• Regenerative Analysis and Steady State Distributions for Markov Chains
• Numerical Computation of the Matrix Exponential with Accuracy Estimate
• The Sensitivity of the Matrix Exponential
• Expokit
• Phase-type distributions: open problems and a few properties
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• A proof of the steepest increase conjecture of a phase-type density
• Condition Estimates for Matrix Functions
• On Two-Sided Bounds Related to Weakly Diagonally Dominant M-Matrices with Application to Digital Circuit Dynamics
• The Scaling and Squaring Method for the Matrix Exponential Revisited