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| 摘要: |
| 本文研究了M-矩阵代数Riccati方程的求解问题.基于交替线性化隐式迭代法，提出了一类改进的交替线性化隐式迭代法用于计算M-矩阵代数Riccati方程的最小非负解.在一定条件下证明了新方法的收敛性并给出最优参数表达式.数值实验表明，改进的方法在一定条件下是可行的. |
| 关键词: 代数Riccati方程 最小非负解 M-矩阵 ALI迭代法 |
| DOI： |
| 分类号:O241.6 |
| 基金项目:Supported in part by National Natural Science Foundation of China (11401424); Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi (2019L0783); Cultivate Scientific Research Excellence Programs of Higher Education Institutions in Shanxi (2019KJ035). |
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| A MODIFIED ALTERNATELY LINEARIZED IMPLICIT ITERATION METHOD FOR M-MATRIX ALGEBRAIC RICCATI EQUATION |
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GUAN Jin-rui,ZHOU Fang,ZUBAIR Ahmed
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| Abstract: |
| In this paper, we study the numerical solution of M-matrix algebraic Riccati equation. Based on the alternately linearized implicit iteration method, we propose a modified alternately linearized implicit iteration method (MALI) for computing the minimal nonnegative solution of MARE. Convergence of the MALI iteration method is proved under suitable conditions. Convergence rate with optimal parameters are given for the MARE associated with a nonsingular M-matrix or an irreducible singular M-matrix. Numerical experiments are given to show that the MALI iteration method is feasible in some cases. |
| Key words: algebraic Riccati equations minimal nonnegative solution M-matrix ALI iteration method |
