Interval Quadratic Equations: A Review

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...

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Bibliographic Details
Published in:AppliedMath 2023-12, Vol.3 (4), p.909-956
Main Authors: Elishakoff, Isaac, Yvain, Nicolas
Format: Article
Language:English
Subjects:
interval coefficients
interval quadratic equations
interval variables
real roots
uncertain variables
uncertainty
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Summary: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.
ISSN:2673-9909
2673-9909
DOI:10.3390/appliedmath3040048