Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets

Document Type : Research Paper


1 School of Mathematics and Computer Science, Damghan University, Damghan, Iran; Member of Young Researchers Society of Shahid Bahonar University of Kerman, Kerman, P.O. Box 76169-14111, Iran

2 Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran


This paper introduces the interval unilateral quadratic matrix equation, $AX^2+BX+C=0$ and attempts to find various analytical results on its $AE$-solution sets in which $A, B$ and $C$ are known real interval matrices, while $X$ is an unknown matrix. These results are derived from a generalization of some results of Shary. We also give sufficient conditions for non-emptiness of some quasi-solution sets, provided that $A$ is regular. As the most common case, the united solution set has been studied and two direct methods for computing an outer estimation and an inner estimation of the united solution set of an interval unilateral quadratic matrix equation are proposed. The suggested techniques are based on nonlinear programming as well as sensitivity analysis.