On the convergence of Halley’s method for simultaneous computation of polynomial zeros

In this paper we study the convergence of Halley’s method as a method for finding all zeros of a polynomial simultaneously. We present two types of local convergence theorems as well as a semilocal convergence theorem for Halley’s method for simultaneous computation of polynomial zeros.

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Bibliographic Details
Published inJournal of numerical mathematics Vol. 23; no. 4; pp. 379 - 394
Main Authors Proinov, Petko D., Ivanov, Stoil I.
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.12.2015
Walter de Gruyter GmbH
Subjects
Computation
Convergence
error estimates
Halley’s method
local convergence
Mathematical models
polynomial zeros
Polynomials
semilocal convergence
simultaneous methods
Theorems
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Summary:In this paper we study the convergence of Halley’s method as a method for finding all zeros of a polynomial simultaneously. We present two types of local convergence theorems as well as a semilocal convergence theorem for Halley’s method for simultaneous computation of polynomial zeros.
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content type line 23
ISSN:1570-2820
1569-3953
DOI:10.1515/jnma-2015-0026