Polynomial approximation of the high orders

N. D. Dikusar

Matematičeskoe modelirovanie, Tome 27 (2015) no. 9, pp. 89-109

Résumé

A new approach is proposed to high-order polynomial approximation (smoothing), based on the basic elements method (BEM.) The $n^{\mathrm{th}}$-degree BEM-polynomial is expressed using four basic elements given on a three-point grid: $x_0+\alpha$, $\alpha\beta0$. Formulae have been obtained for calculating the coefficients of the 12-th order polynomial model depending on the interval length, the continuous parameters $\alpha$, $\beta$ and the derivatives $f^{(m)}(x_0+\nu)$, $\nu=\alpha, \beta, 0$, $m=\overline{0,3}$. Application of BEM-polynomials of high degrees for piecewise polynomial approximation (PWA) and smoothing enhances the stability and accuracy of calculations, as the grid step increases, and reduces the computing complexity as well.

Détail

Keywords: high degree polynomials, piecewise polynomial approximation, least squares method, basic elements method, smoothing, efficiency of algorithms.
Mots-clés : curve segmentation