Open AccessFamily of simultaneous methods with corrections for approximating zeros of analytic functions
Author(s) -
L. Rančić
Publication year - 2015
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1510217r
Subject(s) - mathematics , convergence (economics) , simple (philosophy) , complex plane , analytic function , class (philosophy) , newton's method , iterative method , plane (geometry) , local convergence , mathematical analysis , mathematical optimization , nonlinear system , geometry , computer science , philosophy , physics , epistemology , quantum mechanics , artificial intelligence , economics , economic growth
A family of accelerated iterative methods for the simultaneous approximation of complex zeros of a class of analytic functions is proposed. Considered analytic functions have only simple zeros inside a simple smooth closed contour in the complex plane. It is shown that the order of convergence of the basic family can be increased from four to five and six using Newton?s and Halley?s corrections, respectively. The improved convergence is achieved on the account of additional calculations of low computational cost, which significantly increases the computational efficiency of the accelerated methods. Numerical examples demonstrate a good convergence properties, fitting very well theoretical results.