The maximal positive definite solution of the nonlinear matrix equation X + A*X-1 A + B*X-1 B = I

被引：0
|
作者：
Sayevand, Khosro [1 ]
Erfanifar, Raziyeh [1 ]
Esmaeili, Hamid [2 ]
机构：
[1] Malayer Univ, Fac Math & Stat, Malayer, Iran
[2] Bu Ali Sina Univ, Dept Math, Hamadan, Hamadan, Iran
来源：
MATHEMATICAL SCIENCES | 2023年 / 17卷 / 04期
关键词：
Matrix equation; Convergence rate; Inversion free; Fixed point iteration; ITERATIVE METHODS; ALGORITHMS; EXISTENCE; SYSTEM;
D O I：
10.1007/s40096-022-00454-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the current study, we present a new inversion free variant of the fixed point iteration method to find a maximal positive definite solution for the matrix equation X + A*X-1 A + B*X-1 B = I. The existence conditions of the nonlinear matrix equation are derived. Some numerical examples are presented to show the behavior and efficiency of the considered iterative method. The comparison of the results shows that the new algorithm is more accurate and has fewer operations than the other algorithms. Some conclusions and open problems on possible future research direction close the paper.
引用
收藏
页码：337 / 350
页数：14
相关论文
共 50 条
  • [21] NATURE OF HER X-1 AND SCO X-1
    SHKLOVSKIJ, IS
    ASTRONOMICHESKII ZHURNAL, 1973, 50 (02): : 233 - 242
  • [22] On the existence of a positive definite solution of the matrix equation X-A*qq√X-1A = I
    Banha Univ, Banha, Egypt
    International Journal of Computer Mathematics, 2000, 76 (03) : 331 - 338
  • [23] The equation xn-1/x-1=yq has no solution with x square
    Bugeaud, Y
    Mignotte, M
    Roy, Y
    MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1999, 127 : 353 - 372
  • [24] NOISE VARIABILITY IN CYG X-1 AND HER X-1
    BELLONI, T
    HASINGER, G
    PROCEEDINGS OF THE 23RD ESLAB SYMPOSIUM ON TWO TOPICS IN X-RAY ASTRONOMY, VOLS 1 AND 2: X-RAY BINARIES; AGN AND THE X-RAY BACKGROUND, 1989, 296 : 283 - 287
  • [25] On the Sensitivity of the Matrix Equations X +/- A* X-1 A = Q
    Popchev, Ivan
    Angelova, Vera
    CYBERNETICS AND INFORMATION TECHNOLOGIES, 2010, 10 (04) : 36 - 61
  • [26] Positive definite solution of the matrix equation X = Q − A∗X −1A + B∗X −1B via Bhaskar-Lakshmikantham fixed point theorem
    Maher Berzig
    Xuefeng Duan
    Bessem Samet
    Mathematical Sciences, 2012, 6 (1)
  • [27] An algorithm for computing positive definite solutions of the nonlinear matrix equation X+A*X-1A=I
    El-Sayed, S
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2003, 80 (12) : 1527 - 1534
  • [28] The Hermitian Positive Definite Solution of Matrix Equations X+A.X-1A = I
    Wei, Peiyu
    Tan, Boxue
    Liu, Xueting
    2009 2ND IEEE INTERNATIONAL CONFERENCE ON COMPUTER SCIENCE AND INFORMATION TECHNOLOGY, VOL 4, 2009, : 497 - +
  • [29] Positive definite solution of the matrix equation X = Q - AX(-1)A
    Berzig, Maher
    Duan, Xuefeng
    Samet, Bessem
    MATHEMATICAL SCIENCES, 2012, 6 (01)
  • [30] The Hermitian Positive Definite Solution of a Type of Nonlinear Matrix Equations X plus A*X-1A=I
    Wei, Peiyu
    Tan, Boxue
    Liu, Xueting
    2009 2ND IEEE INTERNATIONAL CONFERENCE ON COMPUTER SCIENCE AND INFORMATION TECHNOLOGY, VOL 4, 2009, : 135 - +
12345