ON THE NONLINEAR MATRIX EQUATION (0<q≤1) Yin, Xiaoyan; Wen, Ruiping; Fang, Liang;
Abstract
In this paper, the nonlinear matrix equation < 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.
Convergence analysis of some iterative methods for a nonlinear matrix equation, Computers & Mathematics with Applications, 2016, 72, 4, 1164
2.
Positive definite solutions and perturbation analysis of a class of nonlinear matrix equations, Journal of Applied Mathematics and Computing, 2017, 53, 1-2, 245
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