Numerical Results on the Zeros of Generalized Fibonacci Polynomials

Matthew He; P. E. Ricci; D. S. Simon

Numerical Results on the Zeros of Generalized Fibonacci Polynomials

Matthew He
, P. E. Ricci
, D. S. Simon

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Pages (from-to)	25-40
Journal	Calcolo: A Quarterly on Numerical Analysis and Theory of Computation
Volume	34
Issue number	1-4
State	Published - Jan 1 1997

Disciplines

Mathematics

Cite this

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title = "Numerical Results on the Zeros of Generalized Fibonacci Polynomials",

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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year = "1997",

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AU - Ricci, P. E.

AU - Simon, D. S.

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N2 - 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.

AB - 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.

UR - https://nsuworks.nova.edu/math_facarticles/184

M3 - Article

SN - 0008-0624

VL - 34

SP - 25

EP - 40

JO - Calcolo: A Quarterly on Numerical Analysis and Theory of Computation

JF - Calcolo: A Quarterly on Numerical Analysis and Theory of Computation

IS - 1-4

ER -

Numerical Results on the Zeros of Generalized Fibonacci Polynomials

Abstract

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