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A Realistic Tolerant Solution of a System of Interval Linear Equations with the Use of Multidimensional Interval Arithmetic Cover

A Realistic Tolerant Solution of a System of Interval Linear Equations with the Use of Multidimensional Interval Arithmetic

Open Access
|Jun 2023

Abstract

The paper presents a method of determining the robustness of solutions of systems of interval linear equations (ILEs). The method can be applied also for the ILE systems for which it has been impossible to find solutions so far or for which solutions in the form of improper intervals have been obtained (which cannot be implemented in practice). The research conducted by the authors has shown that for many problems it is impossible to arrive at ideal solutions that would be fully robust to data uncertainty. However, partially robust solutions can be obtained, and those with the highest robustness can be selected and put into practice. The paper shows that the degree of robustness to the uncertainty of the entire system can be calculated on the basis of the degrees of robustness of individual equations, which greatly simplifies calculations. The presented method is illustrated with a series of examples (also benchmark ones) that facilitate its understanding. It is an extension of the authors’ previously published method for first-order ILEs.

DOI: https://doi.org/10.34768/amcs-2023-0018 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 229 - 247
Submitted on: Jul 26, 2022
Accepted on: Feb 2, 2023
Published on: Jun 23, 2023
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2023 Andrzej Piegat, Marcin Pluciński, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.