On the Matrix Equation X = Q − SX†S

On the Matrix Equation X = Q − SX†S

The positive semidefinite solutions of the nonlinear matrix equation X + S* X†S = Q are investigated. We consider an iterative method converges to a positive semidefinite solution of this equation under the condition Ker X ⊆ Ker S*. The new results are illustrated by numerical examples.

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Veröffentlicht in:Numerical functional analysis and optimization 2007-04, Vol.28 (3-4), p.353-365
1. Verfasser: Ivanov, Ivan Ganchev
Format: Artikel
Sprache:eng
Schlagworte:
Nonlinear matrix equation
Positive semidefinite solution
Pseudo-inverse matrix
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Zusammenfassung:The positive semidefinite solutions of the nonlinear matrix equation X + S* X†S = Q are investigated. We consider an iterative method converges to a positive semidefinite solution of this equation under the condition Ker X ⊆ Ker S*. The new results are illustrated by numerical examples.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630560701250036