求解非对称耦合代数Riccati方程的改进迭代法

IF 0.6 4区数学 Q3 MATHEMATICS

Taiwanese Journal of Mathematics Pub Date : 2023-01-01 DOI:10.11650/tjm/231101

Li Wang, Yibo Wang

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引用次数: 0

摘要

本文导出了求解非对称耦合代数Riccati方程(NCARE)的改进交替线性隐式迭代法。在MALI迭代算法中，线性矩阵方程的系数矩阵在每个迭代步都是固定的。此外，MALI迭代方法利用最后一步和当前步骤中估计的加权平均值来更新下一个迭代步骤中的估计。进一步给出了改进算法的收敛性理论。最后，通过数值算例验证了该算法的有效性和可行性。

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A Modified Iterative Method for Solving the Non-symmetric Coupled Algebraic Riccati Equation

In this paper, a modified alternately linear implicit (MALI) iteration method is derived for solving the non-symmetric coupled algebraic Riccati equation (NCARE). In the MALI iteration algorithm, the coefficient matrices of the linear matrix equations are fixed at each iteration step. In addition, the MALI iteration method utilizes a weighted average of the estimates in both the last step and current step to update the estimates in the next iteration step. Further, we give the convergence theory of the modified algorithm. Last, numerical examples demonstrate the effectiveness and feasibility of the derived algorithm.

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来源期刊

Taiwanese Journal of Mathematics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

3 months

期刊介绍： The Taiwanese Journal of Mathematics, published by the Mathematical Society of the Republic of China (Taiwan), is a continuation of the former Chinese Journal of Mathematics (1973-1996). It aims to publish original research papers and survey articles in all areas of mathematics. It will also occasionally publish proceedings of conferences co-organized by the Society. The purpose is to reflect the progress of the mathematical research in Taiwan and, by providing an international forum, to stimulate its further developments. The journal appears bimonthly each year beginning from 2008.