On a matrix equation
Abstract
In this paper, we consider one matrix equation that involves a matrix generalization of the the weighted geometric mean. More precisely, for positive definite matrices A and B , for nonsingular matrices M 1 ; M 2 ; : : : ; M m , we show that the following equation has a unique positive definite solution. We also study the multi-step stationary iterative method for this equation and prove the corresponding convergence.