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Positive definite solutions of the matrix equations

✍ Scribed by Xiaoyan Yin; Sanyang Liu

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
393 KB
Volume
59
Category
Article
ISSN
0898-1221

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✦ Synopsis

In this paper we investigate nonlinear matrix equations X Β± A * X -q A = Q where q β‰₯ 1.

We derive necessary conditions and sufficient conditions for the existence of positive definite solutions for these equations. We provide a sufficient condition for the equation X + A * X -q A = Q to have two different positive definite solutions and several sufficient conditions for the equation X -A * X -q A = Q to have a unique positive definite solution. We also propose iterative methods for obtaining positive definite solutions of these equations. Numerical examples are given to illustrate the effectiveness of the methods.

πŸ“œ SIMILAR VOLUMES

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The two matrix equations X s + A T X -t A = I n and X s -A T X -t A = I n are studied. Based on the fixed-point theory, the existence of the symmetric positive definite solutions are proved. Sensitivity analysis of the maximal solution is presented. Some elegant estimates of the positive definite so

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A conjecture that the nonlinear matrix equation always has a unique Hermitian positive definite solution is proved. Some bounds of the unique Hermitian positive definite solution are given.

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✍ Jing Cai; Guoliang Chen πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 162 KB

In this paper, the Hermitian positive definite solutions of the matrix equation X s + A \* X -t A = Q are considered, where Q is an Hermitian positive definite matrix, s and t are positive integers. Necessary and sufficient conditions for the existence of an Hermitian positive definite solution are