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Properties of positive definite solutions of the equation X + A∗X−2A = I

✍ Scribed by Ivan G. Ivanov; Salah M. El-sayed

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
554 KB
Volume
279
Category
Article
ISSN
0024-3795

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✦ Synopsis

In this Paper we discuss some properties of a positive definite Solution of the matrix equation X + A'X-'A = 1. Two effective iterative methods for computing a positive definite Solution of this equation are proposed.

Necessary and sufficient conditions for existente of a positive definite Solution are derived. Numerital experiments are executed with these methods.

📜 SIMILAR VOLUMES

On Hermitian positive definite solutions
On Hermitian positive definite solutions of matrix equation X+A*X−2A=I
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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

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In this paper we consider the positive definite solutions of nonlinear matrix equation X + A ૽ X -δ A = Q, where δ ∈ (0, 1], which appears for the first time in [S.M. El-Sayed, A.C.M. Ran, On an iteration methods for solving a class of nonlinear matrix equations, SIAM J. Matrix Anal. Appl. 23 (2001)

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## Abstract In this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equation __X__ + __A__^\*^__X__^−α^__A__ = __Q__ with α ∈ (0, ∞) are given. Iterative methods to obtain the positive definite solutions are established and the rat