Skip to main content

On the numerical stability of the second barycentric formula for trigonometric interpolation in shifted equispaced points

Austin, Anthony P., Xu, Kuan (2017) On the numerical stability of the second barycentric formula for trigonometric interpolation in shifted equispaced points. IMA Journal of Numerical Analysis, 37 (3). pp. 1355-1374. ISSN 0272-4979. (doi:10.1093/imanum/drw038) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided)

PDF - Publisher pdf
Restricted to Repository staff only
Contact us about this Publication Download (414kB)
[img]
Official URL
http://doi.org/10.1093/imanum/drw038

Abstract

We consider the numerical stability of the second barycentric formula for evaluation at points in [0,2?] of trigonometric interpolants in an odd number of equispaced points in that interval. We show that, contrary to the prevailing view, which claims that this formula is always stable, it actually possesses a subtle instability that seems not to have been noticed before. This instability can be corrected by modifying the formula. We establish the forward stability of the resulting algorithm by using techniques that mimic those employed previously by Higham (2004, The numerical stability of barycentric Lagrange interpolation. IMA J. Numer. Anal., 24, 547–556) to analyse the second barycentric formula for polynomial interpolation. We show how these results can be extended to interpolation on other intervals of length-2? in many cases. Finally, we investigate the formula for an even number of points and show that, in addition to the instability that affects the odd-length formula, it possesses another instability that is more difficult to correct.

Item Type: Article
DOI/Identification number: 10.1093/imanum/drw038
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Kuan Xu
Date Deposited: 09 Nov 2016 18:02 UTC
Last Modified: 29 May 2019 18:09 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/58500 (The current URI for this page, for reference purposes)
  • Depositors only (login required):

Downloads

Downloads per month over past year