Nonsymmetric Algebraic Riccati Equations and Wiener-Hopf Factorization for M-Matrices
- Chun-Hua Guo
- MathematicsSIAM Journal on Matrix Analysis and Applications
- 2001
It is explained how the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation for which the four coefficient matrices form an M-matrix can be found by the Schur method and compared with Newton's method and basic fixed-point iterations.
Iterative solution of two matrix equations
- Chun-Hua Guo, P. Lancaster
- MathematicsMathematics of Computation
- 1 October 1999
Newton's method and inversion free variants of the basic fixed point iteration are discussed in some detail for the first equation andumerical results are reported to illustrate the convergence behaviour of various algorithms.
On the Iterative Solution of a Class of Nonsymmetric Algebraic Riccati Equations
- Chun-Hua Guo, A. Laub
- MathematicsSIAM Journal on Matrix Analysis and Applications
- 1 May 2000
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 of any equation in this class of nonsymmetric algebraic Riccati equations.
Iterative Solution of a Nonsymmetric Algebraic Riccati Equation
- Chun-Hua Guo, N. Higham
- MathematicsSIAM Journal on Matrix Analysis and Applications
- 1 March 2007
The Latouche-Ramaswami algorithm, combined with a shift technique suggested by He, Meini, and Rhee, is breakdown-free and is able to find the minimal solution more efficiently and more accurately than the algorithm without a shift.
On the Doubling Algorithm for a (Shifted) Nonsymmetric Algebraic Riccati Equation
- Chun-Hua Guo, B. Iannazzo, B. Meini
- MathematicsSIAM Journal on Matrix Analysis and Applications
- 1 November 2007
Nonsymmetric algebraic Riccati equations for which the four coefficient matrices form an irreducible singular $M$-matrix, which arises in the study of Markov models, are considered.
A SCHUR–NEWTON METHOD FOR THE MATRIX PTH ROOT AND ITS INVERSE∗
- Chun-Hua Guo, N. Higham
- Mathematics
- 2005
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 cI for c ∈ R then the iteration…
Newton's Method for Discrete Algebraic Riccati Equations when the Closed-Loop Matrix Has Eigenvalues on the Unit Circle
- Chun-Hua Guo
- MathematicsSIAM Journal on Matrix Analysis and Applications
- 1 April 1999
The linear convergence appears to be dominant, and the efficiency of the Newton iteration can be improved significantly by applying a double Newton step at the right time.
Detecting and Solving Hyperbolic Quadratic Eigenvalue Problems
- Chun-Hua Guo, N. Higham, F. Tisseur
- MathematicsSIAM Journal on Matrix Analysis and Applications
- 1 October 2008
An efficient algorithm is obtained that identifies and solves a hyperbolic or overdamped QEP maintaining symmetry throughout and guaranteeing real computed eigenvalues.
Algorithms for hyperbolic quadratic eigenvalue problems
- Chun-Hua Guo, P. Lancaster
- MathematicsMathematics of Computation
- 16 February 2005
It is shown that a relatively efficient test forhyperbolicity can be obtained by computing the eigenvalues of the QEP, and that a hyperbolic QEP is overdamped if and only if its largest eigenvalue is nonpositive.
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