Title
A modification of Newton's method for analytic mappings having multiple zeros A modification of Newton's method for analytic mappings having multiple zeros
Author
Faculty/Department
Faculty of Social Sciences. Communication Sciences
Publication type
article
Publication
Wien ,
Subject
Mathematics
Source (journal)
Computing: archives for informatics and numerical computation. - Wien
Volume/pages
62(1999) :2 , p. 129-145
ISSN
0010-485X
ISI
000080453400003
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Abstract
We propose a modification of Newtons method for computing multiple roots of systems of analytic equations. Under mild assumptions the iteration converges quadratically. It involves certain constants whose product is a lower bound for the multiplicity of the root. As these constants are usually not known in advance, we devise an iteration in which not only an approximation for the root is refined, but also approximations for these constants. Numerical examples illustrate the effectiveness of our approach.
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