A new inversion-free method for a rational matrix equation (Q972782)

The authors consider the problem of finding the minimal Hermitian positive definite solution of the rational matrix equation, \(X+A^* X^{-1}A = I\), where \(A\) is an \(n\) by \(n\) real or complex nonsingular matrix and \(I\) is the identity matrix of order \(n\). The authors develop and analyze a new inversion-free method for the problem. Some numerical results are presented to compare the new method with some previously developed inversion-free methods.