TY - JOUR
ID - 2796
TI - Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Haqiri, Tayyebe
AU - Rivaz, Azim
AU - Mohseni Moghadam, Mahmoud
AD - 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
AD - Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Y1 - 2017
PY - 2017
VL - 8
IS - 2
SP - 223
EP - 241
KW - AE-solution sets
KW - interval unilateral quadratic matrix equation
KW - united solution set
KW - nonlinear programming
KW - Sensitivity analysis
DO - 10.22075/ijnaa.2017.10778.1523
N2 - 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.
UR - https://ijnaa.semnan.ac.ir/article_2796.html
L1 - https://ijnaa.semnan.ac.ir/article_2796_50bf006dbe46ff6c42b14348865a347c.pdf
ER -