𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A derivative free iterative method for finding multiple roots of nonlinear equations

✍ Scribed by Beong In Yun

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
485 KB
Volume
22
Category
Article
ISSN
0893-9659

No coin nor oath required. For personal study only.

✦ Synopsis

For an equation f (x) = 0 having a multiple root of multiplicity m > 1 unknown, we propose a transformation which converts the multiple root to a simple root of H (x) = 0. The transformed function H (x) of f (x) with a small > 0 has appropriate properties in applying a derivative free iterative method to find the root. Moreover, there is no need to choose a proper initial approximation. We show that the proposed method is superior to the existing methods by several numerical examples.

πŸ“œ SIMILAR VOLUMES

Accelerating generators of iterative met
Accelerating generators of iterative methods for finding multiple roots of nonlinear equations
✍ M.S. PetkoviΔ‡; L.D. PetkoviΔ‡; J. DΕΎuniΔ‡ πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 397 KB

a b s t r a c t Two accelerating generators that produce iterative root-finding methods of arbitrary order of convergence are presented. Primary attention is paid to algorithms for finding multiple roots of nonlinear functions and, in particular, of algebraic polynomials. First, two classes of algor

A globally convergent derivative-free me
A globally convergent derivative-free method for solving large-scale nonlinear monotone equations
✍ Qin-Rong Yan; Xiao-Zhen Peng; Dong-Hui Li πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 294 KB

In this paper, we propose two derivative-free iterative methods for solving nonlinear monotone equations, which combines two modified HS methods with the projection method in Solodov and Svaiter (1998) . The proposed methods can be applied to solve nonsmooth equations. They are suitable to large-sca