Volume 23, Issue 4
On Hermitian Positive Definite Solutions of Matrix Equation X-A*X^{-2}A=I

Yu-Hai Zhang

DOI:

J. Comp. Math., 23 (2005), pp. 408-418

Published online: 2005-08

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  • 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.

  • Keywords

Matrix equation Positive definite solution Iterative methods

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@Article{JCM-23-408, author = {}, title = {On Hermitian Positive Definite Solutions of Matrix Equation X-A*X^{-2}A=I}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {4}, pages = {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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8827.html} }
TY - JOUR T1 - On Hermitian Positive Definite Solutions of Matrix Equation X-A*X^{-2}A=I JO - Journal of Computational Mathematics VL - 4 SP - 408 EP - 418 PY - 2005 DA - 2005/08 SN - 23 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/jcm/8827.html KW - Matrix equation KW - Positive definite solution KW - Iterative methods AB - 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.
Yu-Hai Zhang. (1970). On Hermitian Positive Definite Solutions of Matrix Equation X-A*X^{-2}A=I. Journal of Computational Mathematics. 23 (4). 408-418. doi:
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