The stability of barycentric interpolation at the Chebyshev points of the second kind

We present a new analysis of the stability of the first and second barycentric formulae for interpolation at the Chebyshev points of the second kind. Our theory shows that the second formula is more stable than previously thought and our experiments confirm its stability in practice.We also extend o...

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Veröffentlicht in:	Numerische Mathematik 2014-10, Vol.128 (2), p.265-300
1. Verfasser:	Mascarenhas, Walter F.
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Numerical Analysis Numerical and Computational Physics Simulation Theoretical
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Beschreibung
Zusammenfassung:	We present a new analysis of the stability of the first and second barycentric formulae for interpolation at the Chebyshev points of the second kind. Our theory shows that the second formula is more stable than previously thought and our experiments confirm its stability in practice.We also extend our current understanding regarding the accuracy problems of the first barycentric formula.
ISSN:	0029-599X 0945-3245
DOI:	10.1007/s00211-014-0612-6