Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Short communication: Uniqueness of asymptotic solution for general Markov fluid models
Performance Evaluation
Convergence analysis of a variant of the Newton method for solving nonlinear equations
Computers & Mathematics with Applications
Alternating-directional Doubling Algorithm for $M$-Matrix Algebraic Riccati Equations
SIAM Journal on Matrix Analysis and Applications
On the numerical solution of a structured nonsymmetric algebraic Riccati equation
Performance Evaluation
Monotone convergence of Newton-like methods for M-matrix algebraic Riccati equations
Numerical Algorithms
Journal of Computational and Applied Mathematics
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We consider the nonsymmetric algebraic Riccati equation for which the four coefficient matrices form an M-matrix. Nonsymmetric algebraic Riccati equations of this type appear in applied probability and transport theory. The minimal nonnegative solution of these equations can be found by Newton's method and basic fixed-point iterations. The study of these equations is also closely related to the so-called Wiener--Hopf factorization for M-matrices. We explain how the minimal nonnegative solution can be found by the Schur method and compare the Schur method with Newton's method and some basic fixed-point iterations. The development in this paper parallels that for symmetric algebraic Riccati equations arising in linear quadratic control.