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
On Hermitian positive definite solution of the matrix equation
โ Scribed by Xuefeng Duan; Anping Liao
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 506 KB
- Volume
- 229
- Category
- Article
- ISSN
- 0377-0427
No coin nor oath required. For personal study only.
โฆ Synopsis
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.
๐ SIMILAR VOLUMES
## Abstract In this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equation __X__ + __A__^\*^__X__^โฮฑ^__A__ = __Q__ with ฮฑ โ (0, โ) are given. Iterative methods to obtain the positive definite solutions are established and the rat
The Hermitian positive definite solutions of the matrix equation X + A \* X -2 A = I are studied. A necessary and sufficient condition for existence of solutions is given in case A is normal. The basic fixed point iterations for the equation in case A is nonnormal with A are discussed in some detai
A simple representation of the general rank-constrained Hermitian nonnegative-definite (positive-definite) solution to the matrix equation AXA \* = B is derived. As medium steps, the general Hermitian solution and the general Hermitian nonnegative-definite (positive-definite) solution to the matrix
In this paper we investigate nonlinear matrix equations X ยฑ A \* X -q A = Q where q โฅ 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