A note on the minimal nonnegative solution of a nonsymmetric algebraic Riccati equation

DOI10.1016/S0024-3795(02)00431-7zbMath1017.15005MaRDI QIDQ1855425

Chun-Hua Guo

Publication date: 5 February 2003

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

zbMATH Keywords

Markov chainsminimal nonnegative solutionsWiener-Hopf factorizationM-matricesnonsymmetric algebraic Riccati equations

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Matrix equations and identities (15A24) Positive matrices and their generalizations; cones of matrices (15B48) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68)

Related Items (17)

On the solution of algebraic Riccati equations arising in fluid queues ⋮ On inexact Newton methods based on doubling iteration scheme for non-symmetric algebraic Riccati equations ⋮ Effects of a parameter on a nonsymmetric algebraic Riccati equation ⋮ Numerical study on nonsymmetric algebraic Riccati equations ⋮ Monotone convergence of Newton-like methods for \(M\)-matrix algebraic Riccati equations ⋮ Quadratic vector equations ⋮ On algebraic Riccati equations associated with \(M\)-matrices ⋮ A quadratically convergent algorithm for first passage time distributions in the Markov-modulated Brownian motion ⋮ A convergence result for matrix Riccati differential equations associated with \(m\)-matrices ⋮ Modified alternately linearized implicit iteration method for M-matrix algebraic Riccati equations ⋮ Convergence of the solution of a nonsymmetric matrix Riccati differential equation to its stable equilibrium solution ⋮ Efficient methods for solving a nonsymmetric algebraic Riccati equation arising in stochastic fluid models ⋮ ALGORITHMS FOR RETURN PROBABILITIES FOR STOCHASTIC FLUID FLOWS ⋮ A new class of nonsymmetric algebraic Riccati equations ⋮ Convergence rates of some iterative methods for nonsymmetric algebraic Riccati equations arising in transport theory ⋮ Hitting probabilities and hitting times for stochastic fluid flows ⋮ Solvability and different solutions of the operator equation \(XAX=BX\)

Cites Work

• Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains
• Existence of algebraic matrix Riccati equations arising in transport theory
• On the Iterative Solution of a Class of Nonsymmetric Algebraic Riccati Equations
• Nonsymmetric Algebraic Riccati Equations and Wiener--Hopf Factorization for M-Matrices
• Nonsymmetric Algebraic Riccati Equations and Hamiltonian-like Matrices
• Computing the invariant law of a fluid model
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