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Eighth-order methods with high efficiency index for solving nonlinear equations. (English) Zbl 1183.65051
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.
65H05Single nonlinear equations (numerical methods)
65Y20Complexity and performance of numerical algorithms
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