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Zbl 1183.65051
Liu, Liping; Wang, Xia
Eighth-order methods with high efficiency index for solving nonlinear equations. (English)
[J] Appl. Math. Comput. 215, No. 9, 3449-3454 (2010). ISSN 0096-3003

Summary: We derive a new family of eighth-order methods for solving simple roots of nonlinear equations by using weight function methods. Per iteration these methods require three evaluations of the function and one evaluation of its first derivative, which implies that the efficiency indexes are 1.682. Numerical comparisons are made to show the performance of the derived methods, as shown in the illustration examples.

MSC 2000:: *65H05 Single nonlinear equations (numerical methods)
65Y20 Complexity and performance of numerical algorithms

Keywords: eighth-order convergence; nonlinear equations; weight function methods; convergence order; efficiency index; iterative method; numerical examples; comparison of methods

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Zentralblatt MATH Berlin [Germany]