ON FORMULATION OF LIMITARY SPECTRUM OF BANDED TOEPLITZ MATRICES
Abstract
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.
About the Authors
Svetlana Andreyevna Zolotykh
Don State Technical University.
Russian Federation
Russian Federation
Vladimir Alexeyevich Stukopin
Stukopin, Vladimir Alexeyevich, Don State Technical University.
Russian Federation
Russian Federation
References
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Review
For citations:
Zolotykh S.A., Stukopin V.A. ON FORMULATION OF LIMITARY SPECTRUM OF BANDED TOEPLITZ MATRICES. Vestnik of Don State Technical University. 2012;12(8):5-11. (In Russ.)
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