Open AccessAnother Newton-type method with (k+2) order convergence for solving quadratic equations
Author(s) -
R. Thukral
Publication year - 2016
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v12i9.128
Subject(s) - mathematics , convergence (economics) , newton's method , order (exchange) , quadratic equation , function (biology) , conjecture , type (biology) , series (stratigraphy) , convergence tests , normal convergence , rate of convergence , newton's method in optimization , local convergence , iterative method , mathematical optimization , combinatorics , key (lock) , nonlinear system , computer science , computer security , economic growth , ecology , biology , paleontology , geometry , quantum mechanics , evolutionary biology , physics , finance , economics
In this paper we define another Newton-type method for finding simple root of quadratic equations. It is proved that the new one-point method has the convergence order of k  2 requiring only three function evaluations per full iteration,where k is the number of terms in the generating series. The Kung and Traub conjecture states that the multipoint iteration methods, without memory based on n function evaluations, could achieve maximum convergence order 1 2nï€ but, the new method produces convergence order of nine, which is better than the expected maximum convergence order. Finally, we have demonstrated that our present method is very competitive with the similar methods.