Newton iterations for a non‐symmetric algebraic Riccati equation
Linzhang Lu · Numerical Linear Algebra with Applications · 2004
Abstract The computation of the minimal positive solution of a non‐symmetric algebraic Riccati equation arising in transport theory is considered. It was shown in (SIAM J Matrix Anal Appl, submitted) that this can be done via only computing the minimal positive solution of a vector equation, which is derived from special form of the solutions of the Riccati equation and by exploitation of the special structure of the coefficient matrices of the Riccati equation. In this paper, the Newton method is developed for the vector equation. The Newton method is more simple and efficient than the corresponding Newton method directly for original Riccati equation and can preserve the form that any solution of the Riccati equation must satisfy. Combination of the simple iteration and the Newton iteration is also considered. Numerical examples are given. Copyright © 2004 John Wiley & Sons, Ltd.