%0 Journal Article
%T Positive definite solution of two kinds of nonlinear matrix equations
%A Xuefeng Duan
%A Zhenyun Peng
%A Fujian Duan
%J Surveys in Mathematics and its Applications
%D 2009
%I University Constantin Brancusi of Targu-Jiu
%X Based on the elegant properties of the Thompson metric, we prove that the following two kinds of nonlinear matrix equations X=¦²i=1m  Ai* X¦ÄiAi and X=¦²i=1m (Ai* XAi)¦Äi,  (0<|¦Äi|<1) always have a unique positive definite solution.Iterative methods are proposed to compute the unique positive definite solution. We show that the iterative methods are more effective as ¦Ä=max{|¦Äi|,  i=1,2, ..., m} decreases. Perturbation bounds for the unique positive definite solution are derived in the end.
%K Nonlinear matrix equation
%K Positive definite solution
%K Iterative method
%K Perturbation bound
%K Thompson metric.
%U http://www.utgjiu.ro/math/sma/v04/p15.pdf