Two-Step Relaxation Newton Method for Nonsymmetric Algebraic Riccati Equations Arising from Transport Theory

Two-Step Relaxation Newton Method for Nonsymmetric Algebraic Riccati Equations Arising from Transport Theory

We propose a new idea to construct an effective algorithm to compute the minimal positive solution of the nonsymmetric algebraic Riccati equations arising from transport theory. For a class of these equations, an important feature is that the minimal positive solution can be obtained by computing the minimal positive solution of a couple of fixed-point equations with vector form. Based on the f...

Convergence rates of some iterative methods for nonsymmetric algebraic Riccati equations arising in transport theory

Article history: Received 19 May 2009 Accepted 6 August 2009 Available online 2 September 2009 Submitted by C.K. Li AMS classification: 15A24 65F10

On a Newton-Like Method for Solving Algebraic Riccati Equations

An exact line search method has been introduced by Benner and Byers [IEEE Trans. Autom. Control, 43 (1998), pp. 101–107] for solving continuous algebraic Riccati equations. The method is a modification of Newton’s method. A convergence theory is established in that paper for the Newton-like method under the strong hypothesis of controllability, while the original Newton’s method needs only the ...

Fast verified computation for solutions of algebraic Riccati equations arising in transport theory

Inexact Kleinman-Newton Method for Riccati Equations

In this paper we consider the numerical solution of the algebraic Riccati equation using Newton's method. We propose an inexact variant which allows one control the number of the inner iterates used in an iterative solver for each Newton step. Conditions are given under which the monotonicity and global convergence result of Kleinman also hold for the inexact Newton iterates. Numerical results ...