On the Kung-Traub Conjecture for Iterative Methods for Solving Quadratic Equations

Algorithms

Diyashvir Kreetee Rajiv Babajee¹  Alicia Cordero¹  Juan R. Torregrosa¹ 

[1] Independent Scholar, 65, Captain Pontre Street, Sainte Croix, Port Louis 11708, Mauritius

关键词: quadratic equation;    2-point iterative methods;    Kung-Traub’s conjecture;    efficiency Index;    dynamic behaviour;    systems of equations;   

DOI  :  10.3390/a9010001

来源: mdpi

【 摘 要 】

Kung-Traub’s conjecture states that an optimal iterative method based on d function evaluations for finding a simple zero of a nonlinear function could achieve a maximum convergence order of . We also show that we can develop a higher order method with the same number of function evaluations if we know the asymptotic error constant of the previous method. We prove the local convergence of these methods which we term as Babajee’s Quadratic Iterative Methods and we extend these methods to systems involving quadratic equations. We test our methods with some numerical experiments including an application to Chandrasekhar’s integral equation arising in radiative heat transfer theory.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.