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Interpolatory multipoint methods with memory for solving nonlinear equations. (English) Zbl 1243.65054
Summary: A general way to construct multipoint methods for solving nonlinear equations by using inverse interpolation is presented. The proposed methods belong to the class of multipoint methods with memory. In particular, a new two-point method with memory with the order (5+17)/24·562 is derived. Computational efficiency of the presented methods is analyzed and their comparison with existing methods with and without memory is performed on numerical examples. It is shown that a special choice of initial approximations provides a considerably great accuracy of root approximations obtained by the proposed interpolatory iterative methods.
MSC:
65H05Single nonlinear equations (numerical methods)
65Y20Complexity and performance of numerical algorithms
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