ON FORMULATION OF LIMITARY SPECTRUM OF BANDED TOEPLITZ MATRICES
A problem on the formulation of the limit set for the sequences of increasing Toeplitz matrices eigenvalues (of the limitary spectrum) with the chosen symbol is solved. The limitary spectrum of the banded Toeplitz matrices is described as a semialgebraic set, viz a solution set of some system of alg...
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| Format: | Article |
| Language: | Russian |
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Don State Technical University
2012-12-01
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| Series: | Advanced Engineering Research |
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| Online Access: | https://www.vestnik-donstu.ru/jour/article/view/663 |
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| author | Svetlana Andreyevna Zolotykh Vladimir Alexeyevich Stukopin |
| author_facet | Svetlana Andreyevna Zolotykh Vladimir Alexeyevich Stukopin |
| author_sort | Svetlana Andreyevna Zolotykh |
| collection | DOAJ |
| description | A problem on the formulation of the limit set for the sequences of increasing Toeplitz matrices eigenvalues (of the limitary spectrum) with the chosen symbol is solved. The limitary spectrum of the banded Toeplitz matrices is described as a semialgebraic set, viz a solution set of some system of algebraic equations and inequalities. In the solution to the problem, the multivariate resultant technique is used. An algorithm of the limitary spectrum determination is formulated for the particular case. An example of the limitary spectrum computation for the specific symbol is considered. These results check the classical results by F. Spitzer and P. Schmidt on the description of the limitary spectrum of the non-selfadjoint Toeplitz matrices. It should be pointed out that these classical results are significantly existence theorems, and the problem on the effective computation of limitary spectrum by F. Spitzer and P. Schmidt is not considered. |
| format | Article |
| id | doaj-art-d2c06289ab0e4d13bda954220d0eb828 |
| institution | DOAJ |
| issn | 2687-1653 |
| language | Russian |
| publishDate | 2012-12-01 |
| publisher | Don State Technical University |
| record_format | Article |
| series | Advanced Engineering Research |
| spelling | doaj-art-d2c06289ab0e4d13bda954220d0eb8282025-08-20T02:59:32ZrusDon State Technical UniversityAdvanced Engineering Research2687-16532012-12-01128511655ON FORMULATION OF LIMITARY SPECTRUM OF BANDED TOEPLITZ MATRICESSvetlana Andreyevna Zolotykh0Vladimir Alexeyevich Stukopin1Don State Technical University.Stukopin, Vladimir Alexeyevich, Don State Technical University.A problem on the formulation of the limit set for the sequences of increasing Toeplitz matrices eigenvalues (of the limitary spectrum) with the chosen symbol is solved. The limitary spectrum of the banded Toeplitz matrices is described as a semialgebraic set, viz a solution set of some system of algebraic equations and inequalities. In the solution to the problem, the multivariate resultant technique is used. An algorithm of the limitary spectrum determination is formulated for the particular case. An example of the limitary spectrum computation for the specific symbol is considered. These results check the classical results by F. Spitzer and P. Schmidt on the description of the limitary spectrum of the non-selfadjoint Toeplitz matrices. It should be pointed out that these classical results are significantly existence theorems, and the problem on the effective computation of limitary spectrum by F. Spitzer and P. Schmidt is not considered.https://www.vestnik-donstu.ru/jour/article/view/663banded toeplitz matrices, limitary spectrum, resultant, toeplitz matrix symbol. |
| spellingShingle | Svetlana Andreyevna Zolotykh Vladimir Alexeyevich Stukopin ON FORMULATION OF LIMITARY SPECTRUM OF BANDED TOEPLITZ MATRICES Advanced Engineering Research banded toeplitz matrices, limitary spectrum, resultant, toeplitz matrix symbol. |
| title | ON FORMULATION OF LIMITARY SPECTRUM OF BANDED TOEPLITZ MATRICES |
| title_full | ON FORMULATION OF LIMITARY SPECTRUM OF BANDED TOEPLITZ MATRICES |
| title_fullStr | ON FORMULATION OF LIMITARY SPECTRUM OF BANDED TOEPLITZ MATRICES |
| title_full_unstemmed | ON FORMULATION OF LIMITARY SPECTRUM OF BANDED TOEPLITZ MATRICES |
| title_short | ON FORMULATION OF LIMITARY SPECTRUM OF BANDED TOEPLITZ MATRICES |
| title_sort | on formulation of limitary spectrum of banded toeplitz matrices |
| topic | banded toeplitz matrices, limitary spectrum, resultant, toeplitz matrix symbol. |
| url | https://www.vestnik-donstu.ru/jour/article/view/663 |
| work_keys_str_mv | AT svetlanaandreyevnazolotykh onformulationoflimitaryspectrumofbandedtoeplitzmatrices AT vladimiralexeyevichstukopin onformulationoflimitaryspectrumofbandedtoeplitzmatrices |