A combinatorial construction of high order algorithms for finding polynomial roots of known multiplicity
Authors:
Yi Jin and Bahman Kalantari
Journal:
Proc. Amer. Math. Soc. 138 (2010), 18971906
MSC (2010):
Primary 05E05, 05A15, 65D15; Secondary 65Q05, 65H05
Published electronically:
February 5, 2010
MathSciNet review:
2596023
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: We construct a family of high order iteration functions for finding polynomial roots of a known multiplicity . This family is a generalization of a fundamental family of high order algorithms for simple roots that dates back to Schröder's 1870 paper. It starts with the well known variant of Newton's method and the multiple root counterpart of Halley's method derived by Hansen and Patrick. Our approach demonstrates the relevance and power of algebraic combinatorial techniques in studying rational rootfinding iteration functions.
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Additional Information
Yi Jin
Affiliation:
Quantitative Research, Interest Rate Derivatives, J.P. Morgan, 270 Park Avenue, New York, New York 10017
Email:
yi.x.jin@jpmorgan.com
Bahman Kalantari
Affiliation:
Department of Computer Science, Rutgers University (New Brunswick), Hill CenterBusch Campus, 110 Frelinghuysen Road, Piscataway, New Jersey 08854
Email:
kalantar@cs.rutgers.edu
DOI:
http://dx.doi.org/10.1090/S0002993910103098
Keywords:
Symmetric functions,
generating functions,
recurrence relation,
multiple roots,
rootfinding,
iteration functions
Received by editor(s):
December 4, 2007
Published electronically:
February 5, 2010
Additional Notes:
The main idea of this article was developed in the first author’s Ph.D. dissertation [5], supervised by the second author.
Communicated by:
Peter A. Clarkson
Article copyright:
© Copyright 2010
American Mathematical Society
