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双参数交替法求解非对称代数Riccati方程

发表时间:2019-03-22  浏览量:436  下载量:36
全部作者: 刘慧敏,郭晓霞
作者单位: 中国海洋大学数学科学学院
摘 要: 非对称代数Riccati方程的最小非负解求解问题是数值代数的一个重要课题。本文将求解最小非负解的单参数交替线性隐式迭代(alternating linear implicit iteration,ALI)法和多重线性隐式迭代(multiple linear implicit iteration,MLI)法的思想相结合,引入双参数,提出两种不同的求解最小非负解的双参数交替多重线性隐式迭代(alternating multiple linear implicit iteration,AMLI)法。数值实验结果表明,这两种算法不论在时间上还是迭代次数上都有一定的提高。本文不仅从理论上证明了这两种方法的单调收敛性,而且通过数值算例验证了这两种方法的优越性。
关 键 词: 计算数学;非对称代数Riccati方程;最小非负解;双参数交替隐式迭代法;非奇异的M-矩阵
Title: Double parameter alternately methods for nonsymmetric algebraic Riccati equations
Author: LIU Huimin, GUO Xiaoxia
Organization: School of Mathematical Sciences, Ocean University of China
Abstract: To solve the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation is an important problem in numerical algebra. Based on the combination of the single parameter alternating linear implicit iteration (ALI) method and multiple linear implicit iteration (MLI) method in solving the minimal nonnegative solution, two kinds of double parameter alternating multiple linear implicit iteration (AMLI) methods are proposed to solve the minimal nonnegative solution by introducing double parameters. Numerical experiment results show that these two methods are improved in both time and iteration times. It not only proves the monotonic convergence of the two methods in theory, but also shows the superiority of the two methods through numerical examples.
Key words: computational mathematics; nonsymmetric algebraic Riccati equations; the minimal nonnegative solution; double parameter alternating implicit iteration methods; nonsingular M-matrix
发表期数: 2019年2月第1期
引用格式: 刘慧敏,郭晓霞. 双参数交替法求解非对称代数Riccati方程[J]. 中国科技论文在线精品论文,2019,12(1):18-25.
 
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