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Piecewise polynomial approximation of the sixth order with automatic knots detection

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Abstract

Coefficients of a local segment model for piecewise polynomial approximation of the sixth order are evaluated using values of the function and of its first derivative at three knots of the support. The formulas for coefficients of the function’s expansion in degrees of x-x 0 on a three-point grid are obtained within the recently proposed basic element method. The algorithm for automatic knot detection is developed. Numerical calculations applying quite complicated tests have shown the efficiency of the model with respect to calculation stability, accuracy, and smoothness of approximation.

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Authors and Affiliations

  1. Joint Institute for Nuclear Research, Laboratory of Information Technologies, ul. Joliot Curie 6, Dubna, Moscow, 141980, Russia

    N. D. Dikusar

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  1. N. D. Dikusar
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Original Russian Text © N.D. Dikusar, 2014, published in Matematicheskoe Modelirovanie, 2014, Vol. 26, No. 3, pp. 31–48.

But very often it is important for an error to be reduced to zero within the limits of the interval [1] P. L. Chebyshev

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Dikusar, N.D. Piecewise polynomial approximation of the sixth order with automatic knots detection. Math Models Comput Simul 6, 509–522 (2014). https://doi.org/10.1134/S2070048214050020

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  • DOI: https://doi.org/10.1134/S2070048214050020

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