Geodesic
Polynomial approximation of the high orders
Matematičeskoe modelirovanie, Tome 27 (2015) no. 9, pp. 89-109 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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, $\alpha\beta<0$. 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.
Keywords: high degree polynomials, piecewise polynomial approximation, least squares method, basic elements method, smoothing, efficiency of algorithms.
Mots-clés : curve segmentation 
@article{MM_2015_27_9_a7,
     author = {N. D. Dikusar},
     title = {Polynomial approximation of the high orders},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {89--109},
     year = {2015},
     volume = {27},
     number = {9},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_9_a7/}
}
TY  - JOUR
AU  - N. D. Dikusar
TI  - Polynomial approximation of the high orders
JO  - Matematičeskoe modelirovanie
PY  - 2015
SP  - 89
EP  - 109
VL  - 27
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/MM_2015_27_9_a7/
LA  - ru
ID  - MM_2015_27_9_a7
ER  - 
%0 Journal Article
%A N. D. Dikusar
%T Polynomial approximation of the high orders
%J Matematičeskoe modelirovanie
%D 2015
%P 89-109
%V 27
%N 9
%U http://geodesic.mathdoc.fr/item/MM_2015_27_9_a7/
%G ru
%F MM_2015_27_9_a7
N. D. Dikusar. Polynomial approximation of the high orders. Matematičeskoe modelirovanie, Tome 27 (2015) no. 9, pp. 89-109. http://geodesic.mathdoc.fr/item/MM_2015_27_9_a7/

[1] P. L. Chebyshev, Izbrannye trudy, AN SSSR, M., 1955

[2] Iu. S. Zavialov, B. I. Kvasov, V. L. Miroshnichenko, Metody splain-funktsii, Nauka, M., 1980, 267 pp. | MR

[3] N. D. Dikoussar, “Function parameterization by using 4-point transforms”, Comp. Phys. Commun., 99 (1997), 235–254 | Zbl

[4] N. D. Dikusar, “The Basic Element Method”, Math. Models and Comp. Simulations, 3:4 (2011), 492–507 | MR | MR

[5] N. N. Kalitkin, N. M. Shlyakhov, “B-Splines of Arbitrary Degree”, Doklady Mathematics, 60:1 (1999), 28–31 | MR | Zbl

[6] K. de Bor, Prakticheskoe rukovodstvo po splainam, Per. s angl., Radio i sviaz, M., 1985 | MR

[7] N. D. Dikusar, “Piecewise Polynomial Approximation of the Sixth Order with Automatic Knots Detection”, Math. Models and Comp. Simulations, 6:5 (2014), 509–522 | Zbl

[8] R. Franke, “Scattered Data Interpolation: Tests of Some Methods”, Mathematics of Computation, 38 (1982), 181–200 | MR | Zbl

[9] European Physical Journal, C. Review of Particle Physics, 2000, 235