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Paper details
Number 2 - June 2023
Volume 33 - 2023
A realistic tolerant solution of a system of interval linear equations with the use of multidimensional interval arithmetic
Andrzej Piegat, Marcin Pluciński
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.
Keywords
interval arithmetic, interval linear equation system, tolerable solution, multidimensional interval arithmetic