An efficient inversion-free method for solving the nonlinear matrix equation Xp + Σj=1m Aj*X-qj Aj = Q

被引：12

作者：

Erfanifar, Raziyeh ^{[1
]}

Sayevand, Khosro ^{[1
]}

Hajarian, Masoud ^{[2
]}

机构：

[1] Malayer Univ, Fac Math & Stat, Malayer, Iran

[2] Shahid Beheshti Univ, Fac Math Sci, Dept Appl Math, Tehran, Iran

来源：

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS | 2022年 / 359卷 / 07期

关键词：

POSITIVE-DEFINITE SOLUTION; PARAMETER-ESTIMATION; ITERATIVE ALGORITHM; SYSTEMS;

D O I：

10.1016/j.jfranklin.2022.02.030

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this article, we first introduce the necessary and sufficient conditions for the existence of the solution of nonlinear matrix equation X-p + sigma(m)(j=1) A(j)*X-(qj) A(j) = Q. Then we propose the inversion-free iteration method to find this solution of the nonlinear matrix equation. Finally, the accuracy and effectiveness of the proposed method in compare to some existing algorithms are demonstrated by various numerical examples.(C) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

引用

页码：3071 / 3089

页数：19

共 12 条

[1] An efficient inversion-free method for solving the nonlinear matrix equation Xp+∑j=1mAj*X−qjAj=Q
Erfanifar, Raziyeh
Sayevand, Khosro
Hajarian, Masoud
Journal of the Franklin Institute, 2022, 359 (07) : 3071 - 3089
[2] An improved inversion-free method for solving the matrix equation X + A*X-αA = Q
Zhang, Li
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 253 : 200 - 203
[3] The Inversion-Free Iterative Methods for Solving the Nonlinear Matrix Equation X + AHX-1A + BHX-1B = I
Huang, Na
Ma, Changfeng
ABSTRACT AND APPLIED ANALYSIS, 2013,
[4] On the nonlinear matrix equation X-Σi=1m,Ai*Xδi Ai = Q
Duan, Xuefeng
Liao, Anping
Tang, Bin
LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 429 (01) : 110 - 121
[5] ON THE NONLINEAR MATRIX EQUATION X + Σi=1m Ai* X-q Ai = Q(0 < q ≤ 1)
Yin, Xiaoyan
Wen, Ruiping
Fang, Liang
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2014, 51 (03) : 739 - 763
[6] The positive definite solution of the nonlinear matrix equation Xp = A plus M(B plus X-1)-1M
Meng, Jie
Kim, Hyun-Min
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 322 : 139 - 147
[7] Perturbation Analysis of the Nonlinear Matrix Equation X-Σi=1m Ai*XpiAi=Q
Li, Jing
ABSTRACT AND APPLIED ANALYSIS, 2013,
[8] Comment on "Perturbation Analysis of the Nonlinear Matrix Equation X-Σi=1m Ai*XpiAi = Q"
Berzig, Maher
Karapinar, Erdal
ABSTRACT AND APPLIED ANALYSIS, 2013,
[9] Efficient iterative schemes based on Newton's method and fixed-point iteration for solving nonlinear matrix equation Xp = Q±A(X-1+B)-1AT
Erfanifar, Raziyeh
Hajarian, Masoud
ENGINEERING COMPUTATIONS, 2023, 40 (9/10) : 2862 - 2890
[10] Newton's Iteration Method for Solving the Nonlinear Matrix Equation X+ Si=1mAi*X-1Ai=Q
Li, Chang-Zhou
Yuan, Chao
Cui, An-Gang
MATHEMATICS, 2023, 11 (07)

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