On the Computation of the Zeros of the Bessel Polynomials

Pasquini, L.

doi:10.1007/978-1-4684-7415-2_34

Cited by 5 publications

(1 citation statement)

References 31 publications

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“…We discuss the electrostatic interpretation for several cases and the connection to the energy minimization problem. The method in question differs from that used by Dunster et al [4] and is more akin to an approach developed by Pasquini [14][15][16] and more recently [17]. In Section 2, we present the details of the method.…”

Section: Introductionmentioning

confidence: 99%

A Unified Approach to Computing the Zeros of Orthogonal Polynomials

MOUSSA,

TİPTON

2023

Journal of New Theory

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We present a unified approach to calculating the zeros of the classical orthogonal polynomials and discuss the electrostatic interpretation and its connection to the energy minimization problem. This approach works for the generalized Bessel polynomials, including the normalized reversed variant, as well as the Viet\'e--Pell and Viet\'e--Pell--Lucas polynomials. We briefly discuss the electrostatic interpretation for each aforesaid case and some recent advances. We provide zeros and error estimates for various cases of the Jacobi, Hermite, and Laguerre polynomials and offer a brief discussion of how the method was implemented symbolically and numerically with Maple. In conclusion, we provide possible avenues for future research.

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Section: Introductionmentioning

confidence: 99%

A Unified Approach to Computing the Zeros of Orthogonal Polynomials

MOUSSA,

TİPTON

2023

Journal of New Theory

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Accurate computation of the zeros of the generalized Bessel polynomials

Pasquini

2000

Numerische Mathematik

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A general method for approximating polynomial solutions of second-order linear homogeneous differential equations with polynomial coefficients is applied to the case of the families of differential equations defining the generalized Bessel polynomials, and an algorithm is derived for simultaneously finding their zeros. Then a comparison with several alternative algorithms is carried out. It shows that the computational problem of approximating the zeros of the generalized Bessel polynomials is not an easy matter at all and that the only algorithm able to give an accurate solution seems to be the one presented in this paper. Subject Classification (1991): 65F15, 65F30, 65H20 Mathematics

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