Title of article :
Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets
Author/Authors :
Haqiri, Tayyebe School of Mathematics and Computer Science - Damghan University, Damghan , Rivaz, Azim Department of Applied Mathematics - Faculty of Mathematics and Computer - Shahid Bahonar University of Kerman, Kerman , Mohseni Moghadam, Mahmoud Department of Applied Mathematics - Faculty of Mathematics and Computer - Shahid Bahonar University of Kerman, Kerman
Abstract :
This paper introduces the interval unilateral quadratic matrix equation, AX2 + BX + C = 0 and
attempts to nd 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 suficient 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.
Keywords :
AE-solution sets , interval unilateral quadratic matrix equation , united solution set , nonlinear programming , sensitivity analysis
Journal title :
Astroparticle Physics
