The nonlinear matrix equation with is investigated. We consider two cases of this equation: the case and the case In the case , a new sufficient condition for the existence of a unique positive definite solution for the matrix equation is obtained. A perturbation estimate for the positive definite solution is derived. Explicit expressions of the condition number for the positive definite solution are given. In the case , a new sharper perturbation bound for the unique positive definite solution is derived. A new backward error of an approximate solution to the unique positive definite solution is obtained. The theoretical results are illustrated by numerical examples.
"Solutions and Improved Perturbation Analysis for the Matrix Equation ." Abstr. Appl. Anal. 2013 1 - 12, 2013. https://doi.org/10.1155/2013/575964