"Numerical Results on the Zeros of Generalized Fibonacci Polynomials" by Matthew He, P. E. Ricci et al.
 

Mathematics Faculty Articles

Numerical Results on the Zeros of Generalized Fibonacci Polynomials

Document Type

Article

Publication Date

1-1-1997

Publication Title

Calcolo: A Quarterly on Numerical Analysis and Theory of Computation

ISSN

0008-0624

Volume

34

Issue/No.

1-4

First Page

25

Last Page

40

Abstract

We study some fundamental properties of generalized Fibonacci polynomials, by using the properties and characteristics of classical Fibonacci polynomials as a motivation. We derive the generating function and an explicit representation of these polynomials. A trace relation for a related r×r matrix Q r is derived. We then study the location and distribution of the zeros of the polynomials by illustrating our numerical results and by means of the so-called Newton sum rules.

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