Computing the Extremal Positive Definite Solutions of a Matrix Equation

Authors:
Xingzhi Zhan
Affiliations:
-
Venue:
SIAM Journal on Scientific Computing
Year:
1996

Citing 0
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Abstract

An efficient and numerically stable implementation of a known algorithm is suggested for finding the extremal positive definite solutions of the matrix equation $X+A^*X^{-1}A=I$, if such solutions exist. The convergence rate is analyzed. A new algorithm that avoids matrix inversion is presented. Numerical examples are given to illustrate the effectiveness of the algorithms.