A general family of third order method for finding multiple roots

作者：Sbibih D^*; Serghini A; Tijini A; Zidna A

来源：Applied Mathematics and Computation, 2014, 233: 338-350.

DOI：10.1016/j.amc.2014.01.108

• Newton's method
• Iterative methods
• Order of convergence
• Multiple roots

In this paper, we describe a general family of iterative methods for approximating a multiple root z with multiplicity m of a complex defined function. Almost of the family of the methods existing in the literature that use two-function and one-derivative evaluations are a special choice of this general method. We give some conditions to have the third order of convergence and we discuss how to choose a small asymptotic error constant which may be affect the speed of the convergence. Using Mathematica with its high precision compatibility, we present some numerical examples to confirm the theoretical results.

• 出版日期2014-5-1