Mathematics and Statistics Vol. 10(6), pp. 1229 - 1238
DOI: 10.13189/ms.2022.100609
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Iterative Algorithms for Solving the Partial Eigenvalue Problem for Symmetric Interval Matrixes

Alimzhan A. Ibragimov ^*, Dilafruz N. Khamroeva
Department of Informatics, Faculty of Mathematics and Informatics, Navoi State Pedagogical Institute, Uzbekistan

ABSTRACT

In this paper, we consider iterative methods for solving a partial eigenvalue problem for real symmetric interval matrices. Such matrices have applications in modeling many technical problems where a lot of data suffers from limited variation or uncertainty. In modeling most applied problems, when some parameter values fluctuate with a known amplitude, then it can be considered that it is advisable to use interval methods. The algorithms proposed by us are built on the basis of the power method and its modification, the so-called "Method of scalar products" for solving a partial problem of eigenvalues of an interval symmetric matrix. These methods have not yet been studied in detail and are not justified for interval matrices. In the developed algorithms, boundary matrices are first determined by the Deif theorem, and then a partial eigenvalue problem is solved. We also study the problem of convergence of the power method for boundary matrices of a given interval symmetric matrix. The results of the computational experiment show that the interval eigenvalues obtained by the proposed algorithms are in good agreement with the results obtained by other researchers, and in some cases even better. The obtained numerical results are compared by the number of iterations and the width of the interval solution.

KEYWORDS
Partial Eigenvalue Problem, Real Symmetric Interval Matrices, Power Method, Scalar Product Method, Uncertainty, Interval Analysis, Iterative Algorithms, Outer and Inner Approximation

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Alimzhan A. Ibragimov , Dilafruz N. Khamroeva , "Iterative Algorithms for Solving the Partial Eigenvalue Problem for Symmetric Interval Matrixes," Mathematics and Statistics, Vol. 10, No. 6, pp. 1229 - 1238, 2022. DOI: 10.13189/ms.2022.100609.

(b). APA Format:
Alimzhan A. Ibragimov , Dilafruz N. Khamroeva (2022). Iterative Algorithms for Solving the Partial Eigenvalue Problem for Symmetric Interval Matrixes. Mathematics and Statistics, 10(6), 1229 - 1238. DOI: 10.13189/ms.2022.100609.