Geodesic
A Numerical study of Newton interpolation with extremely high degrees
Kybernetika, Tome 54 (2018) no. 2, pp. 279-288.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In current textbooks the use of Chebyshev nodes with Newton interpolation is advocated as the most efficient numerical interpolation method in terms of approximation accuracy and computational effort. However, we show numerically that the approximation quality obtained by Newton interpolation with Fast Leja (FL) points is competitive to the use of Chebyshev nodes, even for extremely high degree interpolation. This is an experimental account of the analytic result that the limit distribution of FL points and Chebyshev nodes is the same when letting the number of points go to infinity. Since the FL construction is easy to perform and allows to add interpolation nodes on the fly in contrast to the use of Chebyshev nodes, our study suggests that Newton interpolation with FL points is currently the most efficient numerical technique for polynomial interpolation. Moreover, we give numerical evidence that any reasonable function can be approximated up to machine accuracy by Newton interpolation with FL points if desired, which shows the potential of this method.
DOI : 10.14736/kyb-2018-2-0279
Classification : 65-05, 65D05, 97N50
Keywords: polynomial interpolation; Newton interpolation; interpolation nodes; Chebyshev nodes; Leja ordering; fast Leja points 
@article{10_14736_kyb_2018_2_0279,
     author = {Breu{\ss}, Michael and Kemm, Friedemann and Vogel, Oliver},
     title = {A {Numerical} study of {Newton} interpolation with extremely high degrees},
     journal = {Kybernetika},
     pages = {279--288},
     publisher = {mathdoc},
     volume = {54},
     number = {2},
     year = {2018},
     doi = {10.14736/kyb-2018-2-0279},
     mrnumber = {3807715},
     zbl = {06890420},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-2-0279/}
}
TY  - JOUR
AU  - Breuß, Michael
AU  - Kemm, Friedemann
AU  - Vogel, Oliver
TI  - A Numerical study of Newton interpolation with extremely high degrees
JO  - Kybernetika
PY  - 2018
SP  - 279
EP  - 288
VL  - 54
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-2-0279/
DO  - 10.14736/kyb-2018-2-0279
LA  - en
ID  - 10_14736_kyb_2018_2_0279
ER  - 
%0 Journal Article
%A Breuß, Michael
%A Kemm, Friedemann
%A Vogel, Oliver
%T A Numerical study of Newton interpolation with extremely high degrees
%J Kybernetika
%D 2018
%P 279-288
%V 54
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-2-0279/
%R 10.14736/kyb-2018-2-0279
%G en
%F 10_14736_kyb_2018_2_0279
Breuß, Michael; Kemm, Friedemann; Vogel, Oliver. A Numerical study of Newton interpolation with extremely high degrees. Kybernetika, Tome 54 (2018) no. 2, pp. 279-288. doi : 10.14736/kyb-2018-2-0279. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-2-0279/

Cité par Sources :