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

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).

Abstract

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

CLC Number:

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.

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

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