Two Structure-Preserving-Doubling Like Algorithms to Solve the Positive Definite Solution of the Equation X - AHX-1A = Q

doi:10.1007/s42967-020-00062-w

Communications on Applied Mathematics and Computation ›› 2021, Vol. 3 ›› Issue (1): 123-135.doi: 10.1007/s42967-020-00062-w

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Two Structure-Preserving-Doubling Like Algorithms to Solve the Positive Definite Solution of the Equation X - A^HX^-1A = Q

Xiao-Xia Guo, Hong-Xiao Wu

School of Mathematical Science, Ocean University of China, Qingdao 266100, Shandong Province, China

收稿日期:2019-09-08 修回日期:2020-01-07 出版日期:2021-03-20 发布日期:2021-03-15
通讯作者: Xiao-Xia Guo, guoxiaoxia@ouc.edu.cn E-mail:guoxiaoxia@ouc.edu.cn
基金资助:
This research is supported by the National Natural Science Foundation of China (No. 11871444).

Two Structure-Preserving-Doubling Like Algorithms to Solve the Positive Definite Solution of the Equation X - A^HX^-1A = Q

Xiao-Xia Guo, Hong-Xiao Wu

School of Mathematical Science, Ocean University of China, Qingdao 266100, Shandong Province, China

Received:2019-09-08 Revised:2020-01-07 Online:2021-03-20 Published:2021-03-15
Contact: Xiao-Xia Guo, guoxiaoxia@ouc.edu.cn E-mail:guoxiaoxia@ouc.edu.cn
Supported by:
This research is supported by the National Natural Science Foundation of China (No. 11871444).

摘要/Abstract

摘要： In this paper, we study the nonlinear matrix equation X - A^HX^-1A = Q, where A, Q ∈ ℂ^n×n, Q is a Hermitian positive definite matrix and X ∈ ℂ^n×n is an unknown matrix. We prove that the equation always has a unique Hermitian positive definite solution. We present two structure-preserving-doubling like algorithms to find the Hermitian positive definite solution of the equation, and the convergence theories are established. Finally, we show the effectiveness of the algorithms by numerical experiments.

关键词: Positive definite solution, Structure-preserving-doubling like algorithm, Convergence, Numerical experiment

Abstract: In this paper, we study the nonlinear matrix equation X - A^HX^-1A = Q, where A, Q ∈ ℂ^n×n, Q is a Hermitian positive definite matrix and X ∈ ℂ^n×n is an unknown matrix. We prove that the equation always has a unique Hermitian positive definite solution. We present two structure-preserving-doubling like algorithms to find the Hermitian positive definite solution of the equation, and the convergence theories are established. Finally, we show the effectiveness of the algorithms by numerical experiments.

Key words: Positive definite solution, Structure-preserving-doubling like algorithm, Convergence, Numerical experiment

中图分类号:

Xiao-Xia Guo, Hong-Xiao Wu. Two Structure-Preserving-Doubling Like Algorithms to Solve the Positive Definite Solution of the Equation X - A^HX^-1A = Q[J]. Communications on Applied Mathematics and Computation, 2021, 3(1): 123-135.

参考文献

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Two Structure-Preserving-Doubling Like Algorithms to Solve the Positive Definite Solution of the Equation X - A^HX^-1A = Q

Two Structure-Preserving-Doubling Like Algorithms to Solve the Positive Definite Solution of the Equation X - A^HX^-1A = Q

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