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ON THE NONLINEAR MATRIX EQUATION $X+\sum_{i=1}^{m}A_i^*X^{-q}A_i=Q$(0<q≤1)
Yin, Xiaoyan,Wen, Ruiping,Fang, Liang Korean Mathematical Society 2014 대한수학회보 Vol.51 No.3
In this paper, the nonlinear matrix equation $$X+\sum_{i=1}^{m}A_i^*X^{-q}A_i=Q(0<q{\leq}1)$$ 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.
ON THE NONLINEAR MATRIX EQUATION X + ∑m i=1 A iX−qAi = Q(0 < q 1)
Xiaoyan Yin,Ruiping Wen,Liang Fang 대한수학회 2014 대한수학회보 Vol.51 No.3
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.