Some acceleration techniques for calculating the eigenvalues of normal Toeplitz matrices

A. K. Abdikalykov^ab, Kh. D. Ikramov^b, V. N. Chugunov<sup>c

a</sup> Kazakhstan Division of the Moscow State University, ul. Munaitpasova 7, Astana, 010010, Kazakhstan
^b Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia
^c Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

Abstract: Certain techniques that can be used for accelerating the calculation of the eigenvalues of normal Toeplitz matrices are described. The run times of the standard Matlab procedure eig with and without the use of these techniques are compared.

Key words: Toeplitz matrix, $\phi$-circulant, $(T+H)$-matrix, calculation of eigenvalues.

UDC: 519.61

Received: 30.09.2013

DOI: 10.7868/S0044466914120047

 English version: Computational Mathematics and Mathematical Physics, 2014, 54:12, 1761–1764

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