IJPAM: Volume 46, No. 2 (2008)

Invited Lecture Delivered at
Forth International Conference of Applied Mathematics
and Computing (Plovdiv, Bulgaria, August 12-18, 2007)


FAMILY OF ITERATIVE METHODS FOR COMPUTING
THE ZEROS OF ANALYTIC FUNCTIONS

M.S. Petkovic$^1$, D.M. Miloševic$^2$, L.Z. Rancic$^3$
Faculty of Electronic Engineering
University of Niš
P.O. Box 73, 18000 Niš, SERBIA
e-mail: rancicli@eunet.yu


Abstract.We consider a one parameter family of iterative methods for the simultaneous determination of complex zeros of a class of analytic functions which have only simple zeros inside a simple smooth closed contour in the complex plane. The proposed family is based on a cubically convergent family of iterative methods for solving nonlinear equations. The presented convergence analysis shows that the order of convergence of the considered family is four. Numerical examples demonstrate a good convergence properties, fitting very well theoretical results.

Received: August 17, 2007

AMS Subject Classification: 65H05

Key Words and Phrases: family of iterative methods, simultaneous methods, zeros of analytic functions, convergence

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 46
Issue: 2