IJPAM: Volume 60, No. 2 (2010)

EIGENVECTORS OF TOEPLITZ MATRICES UNDER HIGHER
ORDER THREE TERM RECURRENCE AND
CIRCULANT PERTURBATIONS

D. Fortin
L'Institut National de Recherche en Informatique et en Automatique - INRIA
Domaine de Voluceau, Rocquencourt, B.P. 105
Le Chesnay Cedex, 78153, FRANCE
e-mail: Dominique.Fortin@inria.fr


Abstract.For Toeplitz matrices following a higher order three term recurrence between the main diagonal and 2 other diagonals $l$ and $r$ apart, and possibly circulant perturbations, we extend the kernel method for computing analytically eigenvectors along their eigenvalues. Unlike, the tridiagonal case with corner perturbations which involves sine functions, it is related to the $(p+1,p)$-Pascal triangle for the special cases where the diagonals are respectively at distance $l$ and $r=pl$ from the main diagonal.

Received: March 10, 2010

AMS Subject Classification: 15B05, 11C20, 13F25

Key Words and Phrases: three term recurrence, Toeplitz matrices, eigenvalues, formal series

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 60
Issue: 2