A STUDY ON CONVERGENCE OF EXTENDED LEAP-FROGGING NEWTON'S METHOD LOCATING MULTIPLE ZEROS

Abstract

Assuming that a given nonlinear function f : R → R has a zero α with integer multiplicity m ≥ 1 and is sufficiently smooth in a small neighborhood of α, we define extended leapfrogging Newton's method. We investigate the order of convergence and the asymptotic error constant of the proposed method as a function of multiplicity m. Numerical experiments for various test functions show a satisfactory agreement with the theory presented in this paper and are throughly verified via Mathematica programming with its high-precision computability.

This article was migrated from the previous system via automation. The abstract may not be written correctly. Please view the PDF file.