Finding roots by deflated polynomial approximation

T. Nigel Lucas

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A numerical technique is presented which evaluates the roots of polynomials with real coefficients. Features of the method include no complex arithmetic requirements, no need to guess at initial quadratic factor estimates, multiple or nearly equal roots being easily dealt with and a high degree of flexibility in coping with non-convergent iterations. The method is simple to use and is based upon a Routh Array-type algorithm familiar to control engineers. Numerical examples demonstrate its application to various polynomials.
Original languageEnglish
Pages (from-to)819-830
Number of pages12
JournalJournal of the Franklin Institute
Volume327
Issue number5
DOIs
Publication statusPublished - 1990

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Root-finding
Polynomial approximation
Polynomial Approximation
Polynomials
Roots
Polynomial
Guess
Numerical Techniques
Flexibility
Iteration
Engineers
Numerical Examples
Evaluate
Requirements
Coefficient
Estimate
Demonstrate

Cite this

Lucas, T. Nigel. / Finding roots by deflated polynomial approximation. In: Journal of the Franklin Institute. 1990 ; Vol. 327, No. 5. pp. 819-830.
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Finding roots by deflated polynomial approximation. / Lucas, T. Nigel.

In: Journal of the Franklin Institute, Vol. 327, No. 5, 1990, p. 819-830.

Research output: Contribution to journalArticle

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AU - Lucas, T. Nigel

PY - 1990

Y1 - 1990

N2 - A numerical technique is presented which evaluates the roots of polynomials with real coefficients. Features of the method include no complex arithmetic requirements, no need to guess at initial quadratic factor estimates, multiple or nearly equal roots being easily dealt with and a high degree of flexibility in coping with non-convergent iterations. The method is simple to use and is based upon a Routh Array-type algorithm familiar to control engineers. Numerical examples demonstrate its application to various polynomials.

AB - A numerical technique is presented which evaluates the roots of polynomials with real coefficients. Features of the method include no complex arithmetic requirements, no need to guess at initial quadratic factor estimates, multiple or nearly equal roots being easily dealt with and a high degree of flexibility in coping with non-convergent iterations. The method is simple to use and is based upon a Routh Array-type algorithm familiar to control engineers. Numerical examples demonstrate its application to various polynomials.

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