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Chebyshev interpolation for functions with endpoint singularities via exponential and double-exponential transforms

Abstract:

We present five theorems concerning the asymptotic convergence rates of Chebyshev interpolation applied to functions transplanted to either a semi-infinite or an infinite interval under exponential or double-exponential transformations. This strategy is useful for approximating and computing with functions that are analytic apart from endpoint singularities. The use of Chebyshev polynomials instead of the more commonly used cardinal sinc or Fourier interpolants is important because it enables...

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Publication date:
2012-02-05
URN:
uuid:a889083e-3801-4aa0-8d89-d275d97c5b08
Local pid:
oai:eprints.maths.ox.ac.uk:1497

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