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Iterative methods for the extremal positive definite solution of the matrix equation X+A\*X-αA=Q by Zhen-yun Peng; Salah M. El-Sayed; Xiang-lin Zhang is a Mathematics article available to read on EtoBox.

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In this paper, the inversion free variant of the basic fixed point iteration methods for obtaining the maximal positive definite solution of the nonlinear matrix equation X + A \* X -A = Q with the case 0 < 1 and the minimal positive definite solution of the same matrix equation with the case 1 are proposed. Some necessary conditions and sufficient conditions for the existence of positive definite solutions for the matrix equation are derived. Numerical examples to illustrate the behavior of the considered algorithms are also given.

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Author

Zhen-yun Peng; Salah M. El-Sayed; Xiang-lin Zhang

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0377-0427)

Published

2007

Language

EN

Field

Mathematics (Physical Sciences)