A study of accelerated Newton methods for multiple polynomial roots

We analyze and compare several accelerated Newton methods with built in multiplicity estimates. We also introduce the concept of indicator functions and discuss the Crouse-Putt method. It is shown that many of the accelerated Newton methods not only derive from Schröder’s classic approach but are eq...

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Bibliographic Details
Published inNumerical algorithms Vol. 54; no. 2; pp. 219 - 243
Main Authors Galantai, Aurel, Hegedus, Csaba J
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.06.2010
Springer Nature B.V
Subjects
Algebra
Algorithms
Computer Science
Equivalence
Estimates
Mathematical analysis
Mathematical models
Newton methods
Numeric Computing
Numerical Analysis
Original Paper
Polynomials
Roots
Theory of Computation
Polynomials
Multiple zeros
Convergence acceleration
Newton method
Multiplicity estimates
MSC 65H05
Online AccessGet full text
ISSN1017-1398
1572-9265
DOI10.1007/s11075-009-9332-x

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Summary:We analyze and compare several accelerated Newton methods with built in multiplicity estimates. We also introduce the concept of indicator functions and discuss the Crouse-Putt method. It is shown that many of the accelerated Newton methods not only derive from Schröder’s classic approach but are equivalent. The related computational experiments show that the built in multiplicity estimates can significantly decrease the number of Newton iterations, while the error of these estimates may significantly increase.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-009-9332-x