Abstract
An improvement of the iterative methods based on one point iteration function, with or without memory, using n points with the same amount of information in each point and generated by the inverse polynomial interpolation is given. The adaptation of the strategy presented here gives a new iteration function with a new evaluation of the function which increases the local order of convergence dramatically. This method is generalized to r evaluations of the function. This method for the computation of solutions of nonlinear equations is interesting when it is necessary to get high precision because it provides a lower cost when we use adaptive multi-precision arithmetics.
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References
M. Grau, An improvement to the computing of nonlinear equation solutions, Numer. Algorithms 34 (2003) 1–12.
J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer, New York, 1983).
J.F. Traub, Iterative Methods for the Solution of Equations (Prentice-Hall, Englewood Cliffs, NJ, 1964).
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Communicated by H. Woźniakowski
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65H05
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Grau, M., Peris, J.M. Iterative method generated by inverse interpolation with additional evaluations. Numer Algor 40, 33–45 (2005). https://doi.org/10.1007/s11075-005-2264-1
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DOI: https://doi.org/10.1007/s11075-005-2264-1