Surveys in Mathematics and its Applications (Dec 2009)
Positive definite solution of two kinds of nonlinear matrix equations
Abstract
Based on the elegant properties of the Thompson metric, we prove that the following two kinds of nonlinear matrix equations X=Σi=1m Ai* XδiAi and X=Σi=1m (Ai* XAi)δi, (0i|i|, i=1,2, ..., m} decreases. Perturbation bounds for the unique positive definite solution are derived in the end.