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 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.