This article is cited in 1 paper

An eigenvalue problem for a symmetric Toeplitz matrix

Yu. I. Kuznetsov

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences

Abstract: An algorithm is developed which determines eigenvalues for a symmetric Toeplitz matrix. To this end, we substantiate the generality of eigenvalues problems for a symmetric Toeplitz matrix and for a persymmetric Hankel one. The latter is reduced to an eigenvalue problem for a persymmetric Jacobi matrix. In the even order case, the problem reduces to a Jacobi matrix with halved order.

Key words: symmetric Toeplitz matrix, Hankel structure, Jacobi matrix, persymmetric, tranzitivibilty, Sturm theorem, algorithm, polynomials, roots, eigenvalue problem.

UDC: 517.518.36

Received: 11.11.2008

 English version: Numerical Analysis and Applications, 2009, 2:4, 326–329

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