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- Chun-Hua Guo
- SIAM J. Matrix Analysis Applications
- 2001
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… (More)
- Chun-Hua Guo, Alan J. Laub
- SIAM J. Matrix Analysis Applications
- 2000
We consider the iterative solution of a class of nonsymmetric algebraic Riccati equations, which includes a class of algebraic Riccati equations arising in transport theory. For any equation in this class, Newton's method and a class of basic fixed-point iterations can be used to find its minimal positive solution whenever it has a positive solution. The… (More)
- Chun-Hua Guo
- 2005
We consider the nonsymmetric algebraic Riccati equation XM 12 X + XM 11 + i,j=1 is an irreducible singular M-matrix with zero row sums. The equation plays an important role in the study of stochastic fluid models, where the matrix −M is the generator of a Markov chain. The solution of practical interest is the minimal nonnegative solution. This solution may… (More)
- Chun-Hua Guo
- 2002
We study the quadratic matrix equation X 2 − EX − F = 0, where E is diagonal and F is an M-matrix. Quadratic matrix equations of this type arise in noisy Wiener–Hopf problems for Markov chains. The solution of practical interest is a particular M-matrix solution. The existence and uniqueness of M-matrix solutions and numerical methods for finding the… (More)
- Chun-Hua Guo, Bruno Iannazzo, Beatrice Meini
- SIAM J. Matrix Analysis Applications
- 2007
Nonsymmetric algebraic Riccati equations for which the four coefficient matrices form an irreducible M-matrix M are considered. The emphasis is on the case where M is an irreducible singular M-matrix, which arises in the study of Markov models. The doubling algorithm is considered for finding the minimal nonnegative solution, the one of practical interest.… (More)
- Chun-Hua Guo, Nicholas J. Higham
- SIAM J. Matrix Analysis Applications
- 2007
We study the nonsymmetric algebraic Riccati equation whose four coefficient matrices are the blocks of a nonsingular M-matrix or an irreducible singular M-matrix M. The solution of practical interest is the minimal nonnegative solution. We show that Newton's method with zero initial guess can be used to find this solution without any further assumptions. We… (More)
Newton's method for the inverse matrix pth root, A −1/p , has the attraction that it involves only matrix multiplication. We show that if the starting matrix is c −1 I for c ∈ R + then the iteration converges quadratically to A −1/p if the eigenvalues of A lie in a wedge-shaped convex set containing the disc { z : |z −c p | < c p }. We derive an optimal… (More)
- Chun-Hua Guo
- SIAM J. Matrix Analysis Applications
- 2001
We prove a convergence result for an iterative method, proposed recently by B. Meini, for finding the maximal Hermitian positive definite solution of the matrix equation X+A * X −1 A = Q, where Q is Hermitian positive definite. 1. Introduction. Nonlinear matrix equations occur in many applications. Examples of these equations are algebraic Riccati equations… (More)
- Chun-Hua Guo, Peter Lancaster
- Math. Comput.
- 1999
We study iterative methods for finding the maximal Hermitian positive definite solutions of the matrix equations X + A * X −1 A = Q and X − A * X −1 A = Q, where Q is Hermitian positive definite. General convergence results are given for the basic fixed point iteration for both equations. Newton's method and inversion free variants of the basic fixed point… (More)
- Chun-Yueh Chiang, Eric King-Wah Chu, Chun-Hua Guo, Tsung-Ming Huang, Wen-Wei Lin, Shu-Fang Xu
- SIAM J. Matrix Analysis Applications
- 2009
In this paper, we review two types of doubling algorithm and some techniques for analyzing them. We then use the techniques to study the doubling algorithm for three different nonlinear matrix equations in the critical case. We show that the convergence of the doubling algorithm is at least linear with rate 1/2. As compared to earlier work on this topic,… (More)