IJPAM: Volume 67, No. 1 (2011)
EIGENVECTORS OF THREE TERM RECURRENCE
TOEPLITZ MATRICES AND RIORDAN GROUP
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: Dominique.Fortin@inria.fr
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: Dominique.Fortin@inria.fr
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
