An improved method for finding multiple roots and it's multiplicity of nonlinear equations in R

摘要

The aim of this paper is to develop an improved method for finding the multiple roots of nonlinear equations f(x) = 0 in R along with an approximation to it's multiplicity when it is not known explicitly. This is done by first describing a derivative free transformation G(x) of f(x) which reduces the multiple roots of f(x) = 0 to simple roots of G(x) = 0. Then, a second order Newton-type method is used to compute the simple roots of G(x) = 0 and the approximation to the multiplicity of the roots of f(x) = 0. The method is tested on two numerical examples considered by King [R. F. King, A secant method for multiple roots, BIT 17 (1977)321-328] and results obtained are compared. It is found that our method is more efficient than that given by King and obtain multiple roots as well as it's multiplicity much faster. (c) 2008 Elsevier Inc. All rights reserved.