On Hermitian Positive Definite Solutions of Matrix Equation $X-A^*X^{-2}A=I$

doi:2005-JCM-8827

On Hermitian Positive Definite Solutions of Matrix Equation $X-A^*X^{-2}A=I$

$On Hermitian Positive Definite Solutions of Matrix Equation $X-A^*X^{-2}A=I$$

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Year: 2005

Journal of Computational Mathematics, Vol. 23 (2005), Iss. 4 : pp. 408–418

Abstract

The Hermitian positive definite solutions of the matrix equation $X-A^*X^{-2}A=I$ are studied. A theorem for existence of solutions is given for every complex matrix $A$ . A solution in case $A$ is normal is given. The basic fixed point iterations for the equation are discussed in detail. Some convergence conditions of the basic fixed point iterations to approximate the solutions to the equation are given.

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Journal Article Details

Publisher Name: Global Science Press

Language: English

DOI: https://doi.org/2005-JCM-8827

Journal of Computational Mathematics, Vol. 23 (2005), Iss. 4 : pp. 408–418

Published online: 2005-01

AMS Subject Headings:

Pages: 11

Keywords: Matrix equation Positive definite solution Iterative methods.

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