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On the positive definite solutions of nonlinear matrix equation X + A⋆ X−δA = Q

✍ Scribed by Vejdi I. Hasanov; Salah M. El-Sayed

Publisher: Elsevier Science
Year: 2006
Tongue: English
Weight: 105 KB
Volume: 412
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2005.06.026

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✦ Synopsis

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) 632-645]. The necessary and sufficient conditions for the existence of a solution are derived. An iterative algorithm for obtaining the positive definite solutions of the equation is discussed. The error estimations are found.

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✦ Synopsis

On the positive definite solutions of nonlinear matrix equation X + A⋆ X−δA = Q