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Some optimal iterative methods and their with memory variants. (English) Zbl 1315.65047

The paper concerns some optimal iterative methods for solving nonlinear equations. Based on some existing works, the author constructs a new method, which needs only 4 function evaluations per step and achieves the optimal 8th-order accuracy. This result is also proved rigorously. Furthermore, by carefully choosing the free parameter in the method, the author obtains a new method with memory and obtains a much better convergence rate, namely, order 10. Numerical results are presented to confirm the theoretical results.

MSC:

65H05 Numerical computation of solutions to single equations

Software:

Mathematica
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Full Text: DOI

References:

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