Solving a Nonlinear Matrix Equation via a Contraction Principle

摘要

Based on the elegant properties of the Thompson metric, we consider the nonlinear matrix equation X -A* X-r A=Q, (0 < r < l) via a contraction principle, we prove that the equation has a unique positive definite solution. An iterative method is proposed to compute the positive definite solution, and meanwhile its error estimate is given.