A comparison of methods for accelerating convergence of Newton's method for multiple polynomial roots

Authors:
John Michael McNamee
Affiliations:
-
Venue:
ACM SIGNUM Newsletter
Year:
1998

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Abstract

Newton's method for solving polynomial equations converges only linearly to a multiple root. The speed of several methods for accelerating the convergence have been compared numerically. The Madsen-Reid method proved to be the fastest, with the Aitken and Ostrowsky methods close behind.