On the Iterative Solution of a Class of Nonsymmetric Algebraic Riccati Equations

Authors:
Chun-Hua Guo;Alan J. Laub
Affiliations:
-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2000

Citing 0
Cited 7

Efficient methods for solving a nonsymmetric algebraic Riccati equation arising in stochastic fluid models

Journal of Computational and Applied Mathematics
A class of iterative methods for solving nonsymmetric algebraic Riccati equations arising in transport theory

Computers & Mathematics with Applications
General Matrix Pencil Techniques for Solving Discrete-Time Nonsymmetric Algebraic Riccati Equations

SIAM Journal on Matrix Analysis and 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
A modified structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equations from transport theory

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 properties of these iterative methods are studied and some practical issues are addressed. An algorithm is then proposed to find the minimal positive solution efficiently. Numerical results are also given.