Determination of the zeros of a linear combination of generalised polynomials
type: Item
instance of: scholarly article
title: Determination of the zeros of a linear combination of generalised polynomials
zbMATH Open document ID: 0768.65020
DOI: 10.1016/0377-0427(92)90080-H
author: S. Singh
published in: Journal of Computational and Applied Mathematics
publication date: 1993-01-17T00:00:00Z
review text: A generalized Horner algorithm for finding the zeros of a polynomial is derived which is expressed in a more general basis other than in the monomial basis. The general basis polynomials should be generated by a three-term recurrence relation and might be basis dependent. Then an implementation of the algorithm is briefly described which allows for the solution of polynomials expressed in any of twelve bases given in the paper. Finally, some numerical experiments are reported.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 96899
zbMATH Keywords: Horner algorithm
zbMATH Keywords: zeros of a polynomial
zbMATH Keywords: general basis
zbMATH Keywords: three-term recurrence relation
zbMATH Keywords: implementation
zbMATH Keywords: numerical experiments
reviewed by: Nai-Yang Deng
MaRDI profile type: Publication
cites work: A stopping criterion for polynomial root finding
cites work: The accuracy of floating point computers
cites work: On the condition of algebraic equations
cites work: Determination of the Zeros of a Linear Combination of Chebyshev Polynomials
cites work: An Always Convergent Minimization Technique for the Solution of Polynomial Equations
cites work: A comparison of methods for terminating polynomial iterations
cites work: Practical Problems Arising in the Solution of Polynomial Equations
full work available at URL: 0377-0427(92)90080-h
OpenAlex ID: W2014396513
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description: scientific article; zbMATH DE number 96899