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Zbl 1229.65080
Khattri, Sanjay K.; Argyros, Ioannis K.
Sixth order derivative free family of iterative methods. (English)
[J] Appl. Math. Comput. 217, No. 12, 5500-5507 (2011). ISSN 0096-3003

A four-parameter family of sixth order convergent iterative methods for solving nonlinear scalar equations is developed. Methods of the family require evaluation of four functions per iteration. These methods are totally free of derivatives. Convergence analysis shows that the family is sixth order convergent, which is also verified through the numerical work. Though the methods are independent of derivatives, computational results demonstrate that family of methods are efficient and demonstrate equal or better performance as compared with other six order methods, and the classical Newton method.
[Juri M. Rappoport (Moskva)]

MSC 2000:: *65H05 Single nonlinear equations (numerical methods)

Keywords: iterative methods; nonlinear equations; derivative free; convergence order; Newton

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Zentralblatt MATH Berlin [Germany]