Piecewise Polynomial Approximation of the Sixth Order with Automatic Knots Detection

摘要

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.