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ON THE NONLINEAR MATRIX EQUATION X + ∑m i=1 A iX−qAi = Q(0 < q  1)

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In this paper, the nonlinear matrix equation X + m ∑ i=1 A∗ i X−qAi = Q (0 < q  1) is investigated. Some necessary conditions and sufficient conditions for the existence of positive definite solutions for the matrix equation are derived. Two iterative methods for the maximal positive definite solution are proposed. A perturbation estimate and an explicit expression for the condition number of the maximal positive definite solution are obtained. The theoretical results are illustrated by numerical examples.

Abstract

In this paper, the nonlinear matrix equation X + m ∑ i=1 A∗ i X−qAi = Q (0 < q  1) is investigated. Some necessary conditions and sufficient conditions for the existence of positive definite solutions for the matrix equation are derived. Two iterative methods for the maximal positive definite solution are proposed. A perturbation estimate and an explicit expression for the condition number of the maximal positive definite solution are obtained. The theoretical results are illustrated by numerical examples.

참고문헌 (28)

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