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Article information
2021 , Volume 26, ¹ 3, p.61-85
Sharaya I.A., Shary S.P.
Reserve of characteristic inclusion for interval linear systems of relations
In this paper, we consider interval linear inclusions 𝐶𝑥 ⊆ 𝑑 in the Kaucher complete interval arithmetic. These inclusions are important both on their own and because they provide equivalent and useful descriptions for the so-called quantifier solutions and AE-solutions to interval systems of linear algebraic relations of the form 𝐴𝑥 𝜎 𝑏, where 𝐴 is an interval 𝑚 × 𝑛-matrix, 𝑥 ∈ R 𝑛 , 𝑏 is an interval 𝑚-vector, and 𝜎 ∈ {=, ≤, ≥}𝑚. In other words, these are interval systems in which equations and non-strict inequalities can be mixed. Considering the inclusion 𝐶𝑥 ⊆ 𝑑 in the Kaucher complete interval arithmetic allows studing simultaneously and in a uniform way all the different special cases of quantifier solutions and AE-solutions of interval systems of linear relations, as well as using interval analysis methods. A quantitative measure, called the “inclusion reserve”, is introduced to characterize how strong the inclusion 𝐶𝑥 ⊆ 𝑑 is fulfilled. In our work, we investigate its properties and applications. It is shown that the inclusion reserve turns out to be a useful tool in the study of AE-solutions and quantifier solutions of interval linear systems of equations and inequalities. In particular, the use of the inclusion reserve helps to determine the position of a point relative to a solution set, in investigating whether the solution set is empty or not, whether a point is in the interior of the solution set, etc.
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Keywords: interval linear systems, AE-solutions, quantifier solutions, solution set, characteristic inclusion, inclusion reserve, recognizing functional
doi: 10.25743/ICT.2021.26.3.005
Author(s):
Sharaya Irene Alexandrovna
Position: Research Scientist
Office: Institute of Computational Technologies SB RAS
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave, 6
E-mail: sharia@ict.nsc.ru
Shary Sergey Petrovich
Dr. , Senior Scientist
Position: Leading research officer
Office: Institute of Computational Technologies SB RAS
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave, 6
Phone Office: (3832) 30 86 56
E-mail: shary@ict.nsc.ru
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Bibliography link:
Sharaya I.A., Shary S.P. Reserve of characteristic inclusion for interval linear systems of relations // Computational technologies. 2021. V. 26. ¹ 3. P. 61-85
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