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

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Haqiri Tayyebe; Rivaz Azim; Mohseni Moghadam Mahmoud

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Paper Information

Journal: INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS Year:2017 | Volume:8 | Issue:2 Page(s): 223-241

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Title

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

Author(s)

Haqiri Tayyebe | Rivaz Azim | Mohseni Moghadam Mahmoud | Issue Writer Certificate

Keywords

AE-solution sets

interval unilateral quadratic matrix equation

united solution set

nonlinear programming

sensitivity analysis

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 su cient 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.

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APA: Copy

Haqiri, Tayyebe, Rivaz, Azim, & Mohseni Moghadam, Mahmoud. (2017). Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 8(2), 223-241. SID. https://sid.ir/paper/340687/en

Vancouver: Copy

Haqiri Tayyebe, Rivaz Azim, Mohseni Moghadam Mahmoud. Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS[Internet]. 2017;8(2):223-241. Available from: https://sid.ir/paper/340687/en

IEEE: Copy

Tayyebe Haqiri, Azim Rivaz, and Mahmoud Mohseni Moghadam, “Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets,” INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, vol. 8, no. 2, pp. 223–241, 2017, [Online]. Available: https://sid.ir/paper/340687/en

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