On the maximal Hermitian positive definite solutions of the matrix equation X+A*X-1 A=I

摘要

We study several iterative methods for the maximal Hermitian positive definite solutions of the matrix equation x+ A*X-1 A=1. In these methods, we can avoid matrix inversion for every iteration called inversion free variant of the basic point iteration. In the end, a numerical example is given to illustrate the effectiveness of these methods.