On the Existence of extremal positive definite solutions of a class of Nonlinear Matrix Equation

被引：0
作者：
College of Mathematics, Beihua University, Jilin, 132013, China [1 ]
机构：
[1] College of Mathematics, Beihua University, Jilin
来源：
Adv. Intell. Sys. Comput. | 2013年 / 147-154期
关键词：
Extremal positive solution; Iterative methods; Nonlinear matrix equation; Positive definite;
D O I：
10.1007/978-3-642-37502-6_18
中图分类号：
学科分类号：
摘要：
The nonlinear matrix equation, Xr+∑mi=1 Ai*Xδi Ai=Q is studied. A necessary condition for the existence of positive definite solutions of this equation is derived. Based on the Banach fixed point theorem, a sufficient condition for the existence of a unique positive definite solution of this equation is also derived. Iterative methods for obtaining the extremal (maximal-minimal) positive definite solutions of this equation are proposed. © Springer-Verlag Berlin Heidelberg 2013.
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页码：147 / 154
页数：7
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