Convergence analysis of the Newton–Shamanskii method for a nonsymmetric algebraic Riccati equation
Yiqin Lin, Liang Bao · Numerical Linear Algebra with Applications · 2008
Abstract In this paper, we consider the nonsymmetric algebraic Riccati equation arising in transport theory. An important feature of this equation is that its minimal positive solution can be obtained via computing the minimal positive solution of a vector equation. We apply the Newton–Shamanskii method to solve the vector equation. Convergence analysis shows that the sequence of vectors generated by the Newton–Shamanskii method is monotonically increasing and converges to the minimal positive solution of the vector equation. Numerical experiments show that the Newton–Shamanskii method is feasible and effective, and outperforms the Newton method. Copyright © 2008 John Wiley & Sons, Ltd.