On the fast reduction of symmetric rationally generated Toeplitz matrices to tridiagonal form

In this paper two fast algorithms that use orthogonal similarity transformations to convert a symmetric rationally generated Toeplitz matrix to tridiagonal form are developed, as a means of finding the eigenvalues of the matrix efficiently. The reduction algorithms achieve cost efficiency by exploit...

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Bibliographic Details
Published inElectronic transactions on numerical analysis Vol. 35; p. 129
Main Authors Frederix, K, Gemignani, L, Van Barel, M
Format Journal Article
LanguageEnglish
Published Institute of Computational Mathematics 01.01.2009
Subjects
Algebras, Linear
Eigenvalues
Matrices
Italy
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ISSN1068-9613
1097-4067

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Summary:In this paper two fast algorithms that use orthogonal similarity transformations to convert a symmetric rationally generated Toeplitz matrix to tridiagonal form are developed, as a means of finding the eigenvalues of the matrix efficiently. The reduction algorithms achieve cost efficiency by exploiting the rank structure of the input Toeplitz matrix. The proposed algorithms differ in the choice of the generator set for the rank structure of the input Toeplitz matrix. Key words. Toeplitz matrices, eigenvalue computation, rank structures AMS subject classifications. 65F15
ISSN:1068-9613
1097-4067