Practical Need for Algebraic (Equality-Type) Solutions of Interval Equations and for Extended-Zero Solutions

Authors

Ludmila Dymova, Czestochowa University of Technology
Pavel Sevastjanov, Czestochowa University of TechnologyFollow
Andrzej Pownuk, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

7-2017

Comments

Technical Report: UTEP-CS-17-67a

To appear in Proceedings of the 12th International Conference on Parallel Processing and Applied Mathematics PPAM'17, Lublin, Poland, September 10-13, 2017

Abstract

One of the main problems in interval computations is solving systems of equations under interval uncertainty. Usually, interval computation packages consider united, tolerance, and control solutions. In this paper, we explain the practical need for algebraic (equality-type) solutions, when we look for solutions for which both sides are equal. In situations when such a solution is not possible, we provide a justification for extended-zero solutions, in which we ignore intervals of the type [−a, a].