An application of Fibonacci numbers into infinite Toeplitz matrices

an application of fibonacci numbers into infinite toeplitz matrices

the main purpose of this paper is to define a new regular matrix by using fibonacci numbers and to investigate its matrix domain in the classical sequence spaces $ell _{p},ell _{infty },c$ and $c_{0}$, where $1leq p

The Matrices of Fibonacci Numbers

In a recent paper, Kalman [3] derives many interesting properties of generalized Fibonacci numbers. In this paper, we take a different approach and derive some other interesting properties of matrices of generalized Fibonacci numbers. As an application of such properties, we construct an efficient algorithm for computing matrices of generalized Fibonacci numbers. The topic of generalized Fibona...

On the Norms of Toeplitz Matrices Involving k-Fibonacci and k-Lucas Numbers

Toeplitz transforms of Fibonacci sequences

We introduce a matricial Toeplitz transform and prove that the Toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. We investigate the injectivity of this transform and show how this distinguishes the Fibonacci sequence among other recurrence sequences. We then obtain new Fibonacci identities as an application of our transform.

Approximation Numbers of Toeplitz Matrices 3

The kth approximation number s (p) k (A n ) of a complex n n matrix A n is de ned as the distance of A n to the n n matrices of rank at most n k. The distance is measured in the matrix norm associated with the l p norm (1 < p < 1) on C n . In the case p = 2, the approximation numbers coincide with the singular values. We establish several properties of s (p) k (A n ) provided A n is the n n tru...

Spectral factorization of bi-infinite multi-index block Toeplitz matrices

In this paper we formulate a theory of LU and Cholesky factorization of bi-infinite block Toeplitz matrices A = (Ai−j )i,j∈Zd indexed by i, j ∈ Zd and develop two numerical methods to compute such factorizations. © 2002 Elsevier Science Inc. All rights reserved.