IJPAM: Volume 67, No. 1 (2011)

EIGENVECTORS OF THREE TERM RECURRENCE
TOEPLITZ MATRICES AND RIORDAN GROUP

D. Fortin
Applied Mathematics, Computation and Simulation
INRIA - The French National Institute for Research in
Computer Science and Control
Domaine de Voluceau, Rocquencourt, P.O. Box 105
Le Chesnay Cedex, 78153, FRANCE
e-mail: [email protected]


Abstract.Eigenvalues of tridiagonal (including main) Toeplitz matrices are analytically known under some regular distance to the main diagonal. Any eigenvector may be easily computed then, through a backward process; instead, we give an analytical form for each component through the reciprocation of the underlied trinomial. More generally, the connection to the Riordan group follows some bilinear iterative process.

Received: December 17, 2010

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

Key Words and Phrases: three term recurrence, Toeplitz matrices, eigenvalues, power series, Riordan arrays

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 67
Issue: 1