On positive definite solution of a nonlinear matrix equation
Zhenyun Peng, Salah M. El‐Sayed · Numerical Linear Algebra with Applications · 2006
Abstract In this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equationX+A*X−αA=Qwith α ∈ (0, ∞) are given. Iterative methods to obtain the positive definite solutions are established and the rates of convergence of the considered methods are obtained. Copyright © 2006 John Wiley & Sons, Ltd.