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A STRICT SOLUTION SET TO ISLAE

Kachanov Fedor Konstantinovich  (PhD student MIREA – Russian Technological University )

The paper presents a new approach to determining the solution of interval systems of linear algebraic equations (ISAs), which differs from the classical set-theoretic interpretations. The concept of a strict solution set is introduced, which is defined as the set of interval vectors {X} for which the result of the standard interval multiplication [A] ∙ {X} is in the absorption relation with a given right-hand side {B}. This definition is algebraic and computationally oriented, as it allows direct algorithmic verification taking into account machine error. The article also suggests a method for finding {X} and a method for verifying that the resulting solution belongs to a strict set of solutions. In addition to the formal definition and illustrative example, the article examines the areas of practical application of the approach: from sustainable engineering design and solving interval inverse problems to formal verification of algorithms. The results show that a rigorous set of solutions offers a fundamentally new tool for tasks that require mathematically guaranteed results under conditions of parametric uncertainty.

Keywords:ISLAE, interval analysis, interval arithmetic, solution set, interval matrix, interval vector.
 

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Citation link:
Kachanov F. K. A STRICT SOLUTION SET TO ISLAE // Современная наука: актуальные проблемы теории и практики. Серия: Естественные и Технические Науки. -2026. -№02/2. -С. 81-87 DOI 10.37882/2223-2966.2026.02-2.15
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