Nonlinear matrix equations and structured linear algebra

DOI10.1016/j.laa.2005.06.011zbMath1088.15018OpenAlexW2078400985MaRDI QIDQ819146

Beatrice Meini

Publication date: 22 March 2006

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2005.06.011

zbMATH Keywords

Markov chainsToeplitz matricesmatrix \(p\)th rootnonlinear matrix equationsquadratic matrix equationsblock Hessenberg matricespower series matrix equationsqueueing problems

Mathematics Subject Classification ID

Matrix equations and identities (15A24)

Related Items (2)

Solving two generalized nonlinear matrix equations ⋮ The cyclic reduction algorithm: From Poisson equation to stochastic processes and beyond. In memoriam of Gene H. Golub

Uses Software

• na12

Cites Work

• Factorization of measurable matrix functions. Ed. by Georg Heinig. Transl. from the Russian by Bernd Luderer. With a foreword by Bernd Silbermann. (Licensed ed.)
• Introduction to large truncated Toeplitz matrices
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• Computations with infinite Toeplitz matrices and polynomials
• Improved cyclic reduction for solving queueing problems
• A class of iteration methods based on the Moser formula for nonlinear equations in Markov chains
• New convergence results on functional iteration techniques for the numerical solution of M/G/1 type Markov chains
• Inverting block Toeplitz matrices in block Hessenberg form by means of displacement operators: Application to queueing problems
• Solving nonlinear matrix equations arising in tree-like stochastic processes.
• Algorithms for the matrix \(p\)th root
• Solving a Quadratic Matrix Equation by Newton's Method with Exact Line Searches
• Systems of integral equations on a half line with kernels depending on the difference of arguments
• A stable recursion for the steady state vector in markov chains of m/g/1 type
• Introduction to Matrix Analytic Methods in Stochastic Modeling
• A logarithmic reduction algorithm for quasi-birth-death processes
• Matrix-geometric invariant measures for G/M/l type Markov chains
• A Schur Algorithm for Computing Matrix pth Roots
• Numerical analysis of a quadratic matrix equation
• The Matrix Square Root from a New Functional Perspective: Theoretical Results and Computational Issues
• On the Solution of a Nonlinear Matrix Equation Arising in Queueing Problems
• On the solution of block Hessenberg systems
• Numerical Methods for Structured Markov Chains
• On Direct Methods for Solving Poisson’s Equations
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