Interval Quadratic Equations: A Review
College
Engineering and Computer Science
Department
Ocean and Mechanical Engineering
Document Type
Article
Publication/Event/Conference Title
Appliedmath
Publication Status
Version of Record
Abstract
In this study, we tackle the subject of interval quadratic equations and we aim to accurately determine the root enclosures of quadratic equations, whose coefficients constitute interval variables. This study focuses on interval quadratic equations that contain only one coefficient considered as an interval variable. The four methods reviewed here in order to solve this problem are: (i) the method of classic interval analysis used by Elishakoff and Daphnis, (ii) the direct method based on minimizations and maximizations also used by the same authors, (iii) the method of quantifier elimination used by Ioakimidis, and (iv) the interval parametrization method suggested by Elishakoff and Miglis and again based on minimizations and maximizations. We will also compare the results yielded by all these methods by using the computer algebra system Mathematica for computer evaluations (including quantifier eliminations) in order to conclude which method would be the most efficient way to solve problems relevant to interval quadratic equations.
First Page
909
Last Page
956
DOI
10.3390/appliedmath3040048
Publication Date
12-1-2023
Recommended Citation
Elishakoff, Isaac and Yvain, Nicolas, "Interval Quadratic Equations: A Review" (2023). Faculty Scholarship. 172.
https://digitalcommons.fau.edu/faculty_papers/172