ON THE NONLINEAR MATRIX EQUATION X + ∑m i=1 A iX−qAi = Q(0 < q 1)
ON THE NONLINEAR MATRIX EQUATION X + ∑m i=1 A iX−qAi = Q(0 < q 1)
Xiaoyan Yin(Xidian University); Ruiping Wen(Taiyuan Normal University); Liang Fang(Xidian University)
51권 3호, 739~763쪽
초록
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.
- 발행기관:
- 대한수학회
- 분류:
- 수학