Finding a Multiple Zero by Transformations and Newton-Like Methods

Abstract

Many methods for finding a multiple zero $x^ * $ of a function f are based on transforming f to a function T for which $x^ * $ is a simple zero. We give and analyze a general transformation which includes as special cases three transformations given in the literature. Newton-like methods for solving $T(x) = 0$ are examined and we perform comparative computational tests. The class of methods considered is shown to be of limited practical value.