Interpolatory multipoint methods with memory for solving nonlinear equations
Petkovic, Miodrag S.
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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)/2 ≈ 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.
Applied Mathematics and Computation, 218, (2011), 2533–2541 .
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