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.

Keywords

• Nonlinear matrix equation
• Positive definite solution
• Iterative method
• Perturbation bound
• Thompson metric.