Accurate solutions of \(M\)-matrix Sylvester equations

DOI10.1007/s00211-011-0420-1zbMath1245.65053OpenAlexW1971704548MaRDI QIDQ2428544

Jungong Xue, Ren-Cang Li, Shu-fang Xu

Publication date: 26 April 2012

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

Full work available at URL: https://doi.org/10.1007/s00211-011-0420-1

zbMATH Keywords

numerical examplesrelative perturbation theory\(M\)-matrix Sylvester equation

Mathematics Subject Classification ID

Related Items (14)

Condition number and backward errors of nonsymmetric algebraic Riccati equation ⋮ Condition numbers and backward error of a matrix polynomial equation arising in stochastic models ⋮ Iterative and doubling algorithms for Riccati‐type matrix equations: A comparative introduction ⋮ Accurate solutions of \(M\)-matrix algebraic Riccati equations ⋮ Mixed and componentwise condition numbers of nonsymmetric algebraic Riccati equation ⋮ A NEW VERSION OF THE SMITH METHOD FOR SOLVING SYLVESTER EQUATION AND DISCRETE-TIME SYLVESTER EQUATION ⋮ Effective condition numbers and small sample statistical condition estimation for the generalized Sylvester equation ⋮ Two kinds of condition numbers for the quadratic matrix equation ⋮ Highly accurate doubling algorithms for \(M\)-matrix algebraic Riccati equations ⋮ Accurate numerical solution for structured \(M\)-matrix algebraic Riccati equations ⋮ Normwise, mixed and componentwise condition numbers of matrix equation X-∑_{i=1}^p A_i^T XA_i + ∑_{j=1}^q B_j^T XB_j = Q$ ⋮ Accurate numerical solution for shifted \(M\)-matrix algebraic Riccati equations ⋮ Highly accurate doubling algorithm for quadratic matrix equation from quasi-birth-and-death process ⋮ Highly Accurate Latouche-Ramaswami Logarithmic Reduction Algorithm for Quasi-Birth-and-Death Process

Uses Software

• mctoolbox
• Algorithm 432

Cites Work

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• On the ADI method for Sylvester equations
• Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains
• Entrywise perturbation theory for diagonally dominant M-matrices with applications
• Existence of algebraic matrix Riccati equations arising in transport theory
• Entrywise relative perturbation theory for nonsingular \(M\)-matrices and applications
• Accurate solutions of \(M\)-matrix algebraic Riccati equations
• A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation
• On the Iterative Solution of a Class of Nonsymmetric Algebraic Riccati Equations
• Accurate computation of the smallest eigenvalue of a diagonally dominant $M$-matrix
• Nonsymmetric Algebraic Riccati Equations and Wiener--Hopf Factorization for M-Matrices
• Mixed, Componentwise, and Structured Condition Numbers
• The ADI Model Problem
• Regenerative Analysis and Steady State Distributions for Markov Chains
• A Hessenberg-Schur method for the problem AX + XB= C
• Nonsymmetric Algebraic Riccati Equations and Hamiltonian-like Matrices
• Computing the Smallest Eigenvalue of an M-Matrix
• Accuracy and Stability of Numerical Algorithms
• On Accurate Computations of the Perron Root
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Iterative Solution of a Nonsymmetric Algebraic Riccati Equation
• Matrix Equation $XA + BX = C$

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