On Hermitian positive definite solution of the matrix equation X - Sigma(m)(i=1)A(i)*X(r)A(i) = Q

Duan XF; Liao AP

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On Hermitian positive definite solution of the matrix equation X - Sigma(m)(i=1)A(i)*X(r)A(i) = Q

机译：关于矩阵方程X的Hermitian正定解-Sigma（m）（i = 1）A（i）* X（r）A（i）= Q

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摘要

A conjecture that the nonlinear matrix equation X - Sigma(m)(i=1)A(i)*X(r)A(i) = Q (-1 <= r < 0 or 0 < r < 1) always has a unique Hermitian positive definite solution is proved. Some bounds of the unique Hermitian positive definite solution are given.

机译：非线性矩阵方程X-Sigma（m）（i = 1）A（i）* X（r）A（i）= Q（-1 <= r <0或0

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来源
《Journal of Computational and Applied Mathematics》 |2009年第1期|共10页
作者
Duan XF; Liao AP;
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原文格式 PDF
正文语种 eng
中图分类计算数学;
关键词
Nonlinear matrix equation; Hermitian positive definite solution;

机译：非线性矩阵方程;Hermitian正定解;

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2. On Hermitian positive definite solution of the matrix equation X - Sigma(m)(i=1)A(i)*X(r)A(i) = Q [J] . Duan XF, Liao AP Journal of Computational and Applied Mathematics . 2009,第1期

机译：关于矩阵方程X的Hermitian正定解-Sigma（m）（i = 1）A（i）* X（r）A（i）= Q
3. Necessary and Sufficient Conditions for the Existence of a Hermitian Positive Definite Solution of a Type of Nonlinear Matrix Equations [J] . WenlingZhao, HongkuiLi, XuetingLiu, Mathematical Problems in Engineering: Theory, Methods and Applications . 2009,第2期

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4. Equalities and inequalities for Hermitian solutions and Hermitian definite solutions of the two matrix equations AX = B and AXA* = B [J] . Tian Y. Aequationes mathematicae . 2013,第1a2期

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5. The Hermitian Positive Definite Solution of Matrix Equations ions X+A*X-1A=I [C] . Peiyu Wei, Boxue Tan, Xueting Liu IEEE international conference on computer science and information technology;ICCSIT 2009 . 2009

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On Hermitian positive definite solution of the matrix equation X - Sigma(m)(i=1)A(i)*X(r)A(i) = Q

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