Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 783920, 17 pages
Research Article

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

1School of Science, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China
2School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China

Received 26 February 2009; Accepted 20 August 2009

Academic Editor: Alois Steindl

Copyright © 2009 Shulin Wu and Chengming Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 fixed-point vector equations, we introduce a new algorithm, namely, two-step relaxation Newton, derived by combining two different relaxation Newton methods to compute the minimal positive solution. The monotone convergence of the solution sequence generated by this new algorithm is established. Numerical results are given to show the advantages of the new algorithm for the nonsymmetric algebraic Riccati equations in vector form.