IJPAM: Volume 54, No. 1 (2009)

A MODIFIED FAMILY OF LAGUERRE ITERATION
FUNCTIONS OF QUARTICALLY CONVERGENCE

Yoon Mee Ham$^1$, Sang-Gu Lee$^2$, Duk-Sun Kim$^3$
$^1$Department of Mathematics
Kyonggi University
Suwon, 443-760, KOREA
$^{2,3}$Department of Mathematics
Sungkyunkwan University
Suwon, 440-746, KOREA


Abstract.In this paper, we derive a modified family of iteration functions for finding simple zeros of analytic functions. The family includes, Traub's quartic square root method and, as a limiting cases, the Kiss method, the Halley method and the Newton method. We also present a family of third-derivative-free variants of this method. All the methods of the family are locally and quartically convergence for a simple zero. The asymptotic error constants for this methods of the family and numerical examples are given to show the performance of presented methods.

Received: April 14, 2009

AMS Subject Classification: 65-01, 65B99, 65H05

Key Words and Phrases: Laguerre's method, iterative methods, order of convergence

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 1