Solution Form and Simple Iteration of a Nonsymmetric Algebraic Riccati Equation Arising in Transport Theory

Authors:
Lin-Zhang Lu
Affiliations:
-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2005

Citing 0
Cited 5

A class of iterative methods for solving nonsymmetric algebraic Riccati equations arising in transport theory

Computers & Mathematics with Applications
Convergence analysis of a variant of the Newton method for solving nonlinear equations

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On the convergence rate of an iterative method for solving nonsymmetric algebraic Riccati equations

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On inexact Newton methods based on doubling iteration scheme for symmetric algebraic Riccati equations

Journal of Computational and Applied Mathematics
A modified structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equations from transport theory

Journal of Computational and Applied Mathematics

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Abstract

We are interested in computing the minimal positive solution of a nonsymmetric algebraic Riccati equation arising in transport theory. We show that this computation can be done via computing only the minimal positive solution of a vector equation, which is derived from the special form of solutions of the Riccati equation. A simple iterative method is presented for solving the vector equation. The simple iteration is much more efficient than the Gauss--Jacobi method presented by Juang in [Linear Algebra Appl., 230 (1995), pp. 89--100] for the Riccati equation. The symmetric case and bounds of the minimal positive solution are also considered. Numerical experiments are given.