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Explicit eigenvalues of some perturbed heptadiagonal matrices via recurrent sequences

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Abstract

In this paper we present a direct method to calculate explicit expressions of eigenvalues of some perturbed heptadiagonal matrices. The method is of interest to engineers and statisticians since it is based on elementary properties of determinants and recurrent sequences. The use and even the knowledge of the theory of orthogonal polynomials, which was usually necessary (see for example [2]) is not needed here. Once the needed recurent relations are obtained, we use the theory of recurrent sequences and trigonometric formulas.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Qassim University, P. O. Box 6644, Al-Gassim, Buraydah, 51452, Saudi Arabia

    S. Kouachi

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  1. S. Kouachi
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Correspondence to S. Kouachi.

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Submitted by S. N. Tronin

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Kouachi, S. Explicit eigenvalues of some perturbed heptadiagonal matrices via recurrent sequences. Lobachevskii J Math 36, 28–37 (2015). https://doi.org/10.1134/S1995080215010096

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  • DOI: https://doi.org/10.1134/S1995080215010096

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