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A fast, simple, and stable Chebyshev-Legendre transform using an asymptotic formula

Abstract:

A fast, simple, and numerically stable transform for converting between Legendre and Chebyshev coefficients of a degree $N$ polynomial in $O(N(\log N)^{2}/ \log \log N)$ operations is derived. The basis of the algorithm is to rewrite a well-known asymptotic formula for Legendre polynomials of large degree as a weighted linear combination of Chebyshev polynomials, which can then be evaluated by using the discrete cosine transform. Numerical results are provided to demonstrate the efficiency an...

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Nicholas Hale More by this author
Alex Townsend More by this author
Publication date:
2013-08-05
URN:
uuid:70ad6477-670f-49e1-a3fb-54376a7cf726
Local pid:
oai:eprints.maths.ox.ac.uk:1735

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