Algorithms Invenire Asymptotic Formulas Eigenvalues Discreta Semi-Terminus Operators

Methods for finding asymptotic formulas for eigenvalues of discrete semibounded operators given on compact sets are individual in each case. Therefore, it becomes necessary to develop algorithms that allow one to find asymptotic formulas for the eigenvalues of any discrete semi-bounded operators given on compact sets. This will greatly simplify their finding and allow you to write programs to obtain asymptotic formulas. These algorithms will help to find asymptotic formulas for eigenvalues of vector operators given on finite connected graphs.

In the article, based on the methods developed earlier, an algorithm is created that allows finding asymptotic formulas for eigenvalues with any ordinal number for discrete semi-bounded operators given on compact sets. Examples are given of comparing asymptotic formulas found by the developed method and known formulas previously obtained by other authors, which are in good agreement with each other

Keywords

asymptotic formulas; eigenvalues and eigenfunctions of linear operators; discrete semibounded operators.

References

1. Kadchenko S.I., Ryazanova L.S. Numeric Method of Finding the Eigenvalues for the Discrete Lower Semibounded Operators. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2011, no. 17 (234), pp. 46-51. (in Russian)
2. Kadchenko S.I., Zakirova G.A. Calculation of Eigenvalues of Discrete Semibounded Differential Operators. Journal of Computational and Engineering Mathematics, 2017, vol. 4, no. 1, pp. 38-47. DOI: 10.14529/jcem170104
3. Levitan B.M., Sargsyan I.S. Vvedenie v spektral'nuyu teoriyu [Introduction to Spectral Theory]. Moscow, Nauka, 1970. (in Russian)
4. Borg G. Eine Umkehrung der Sturm-Liouvilleschen Elgenvertaufgabe. Acta Mathematica, 1946, vol. 78, no. 2, pp. 1-96. (in German) DOI: 10.1007/BF02421600
5. Behiri S.E., Kazaryan A.R., Khachatryan I.G. [Asymptotic Formula for Eigenvalues of a Regular Two-Term Differential Operator of Arbitrary Even Order]. Scientific Notes of the Yerevan State University. Series: Natural Sciences, 1994, no. 1, pp. 3-18. (in Russian)
6. Mikhaylov V.P. [About Riesz bases in L^2(0,1)]. Academy of Sciences of USSR Reports, 1962, vol. 144, no. 5, pp. 981-984. (in Russian)