A modified Newton-Shamanskii method for a nonsymmetric algebraic Riccati equation

作者：Li, Jian-Lei^*; Zhang, Li-Tao; Li, Xu-Dong; Li, Qing-Bin

来源：Journal of Computational Analysis and Applications, 2016, 21(2): 380-393.

• non-symmetric algebraic Riccati equation
• M-matrix
• transport theory
• minimal positive solution
• modified Newton-Shamanskii method

The non-symmetric algebraic Riccati equation arising in transport theory can be rewritten as a vector equation and the minimal positive solution of the non-symmetric algebraic Riccati equation can be obtained by solving the vector equation. In this paper, based on the Newton-Shamanskii method, we propose a new iterative method called modified Newton-Shamanskii method for solving the vector equation. Some convergence results are presented. The convergence analysis shows that sequence of vectors generated by the modified Newton-Shamanskii method is monotonically increasing and converges to the minimal positive solution of the vector equation. Finally, numerical experiments are presented to illustrate the performance of the modified Newton-Shamanskii method.

• 出版日期2016-8
• 单位常州工学院