On the perturbation estimates of the maximal solution for the matrix equation X + A T √ X −1 A = P
El-Shazly, N. (2016). On the perturbation estimates of the maximal solution for the matrix equation X + A T √ X −1 A = P. EKB Journal Management System, 24(4), 644-649. doi: 10.1016/j.joems.2016.04.004
Naglaa M. El-Shazly. "On the perturbation estimates of the maximal solution for the matrix equation X + A T √ X −1 A = P". EKB Journal Management System, 24, 4, 2016, 644-649. doi: 10.1016/j.joems.2016.04.004
El-Shazly, N. (2016). 'On the perturbation estimates of the maximal solution for the matrix equation X + A T √ X −1 A = P', EKB Journal Management System, 24(4), pp. 644-649. doi: 10.1016/j.joems.2016.04.004
El-Shazly, N. On the perturbation estimates of the maximal solution for the matrix equation X + A T √ X −1 A = P. EKB Journal Management System, 2016; 24(4): 644-649. doi: 10.1016/j.joems.2016.04.004

On the perturbation estimates of the maximal solution for the matrix equation X + A T √ X −1 A = P

Journal of the Egyptian Mathematical Society
Volume 24, Issue 4, 2016, Pages 644-649    PDF (363.28 K)
DOI: 10.1016/j.joems.2016.04.004
Author
Naglaa M. El-Shazly
Department of Mathematics, Faculty of Science, Menoufia University, Shebin El-Koom, Egypt
Abstract
In this paper we investigate the nonlinear matrix equation X + A T
√
X −1 A = P, for the
existence of positive definite solutions. Bounds for  X −1L
 and  X −1  are derived where X L is the
maximal solution and X is any other positive definite solution of this matrix equation. A perturbation
estimate for the maximal solution and an error bound for approximate solutions are derived. A
numerical example is given to illustrate the reliability of the obtained results.
Keywords
Nonlinear matrix equation; Maximal positive solution; Iteration; Perturbation bound
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