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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 \((5 + \sqrt {17})/2 \approx 4.562\) 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:
65H05 Numerical computation of solutions to single equations
65Y20 Complexity and performance of numerical algorithms
Software:
gmp
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