Solutions and Improved Perturbation Analysis for the Matrix Equation

Jing Li

Abstract and Applied Analysis, 2013, vol. 2013, 1-12

Abstract:

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:575964

DOI: 10.1155/2013/575964

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