A numerical study of Newton interpolation with extremely high degrees

Title:

A numerical study of Newton interpolation with extremely high degrees

Creator:

Breuss, Michael, Kemm, Friedemann, and Vogel, Oliver

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:8f2ac8ed-96e6-43bd-be2e-95e68e63c13d
uuid:8f2ac8ed-96e6-43bd-be2e-95e68e63c13d
doi:10.14736/kyb-2018-2-0279

Subject:

polynomial interpolation, Newton interpolation, interpolation nodes, Chebyshev nodes, Leja ordering, and fast Leja points

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Source:

Kybernetika | 2018 Volume:54 | Number:2

Harvested from:

CDK

Metadata only:

false