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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Bibliographic Details
Published inNumerische Mathematik Vol. 128; no. 2; pp. 265 - 300
Main Author Mascarenhas, Walter F.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2014
Subjects
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Simulation
Theoretical
65D05
65G50
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Summary: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