A Fast, Simple, and Stable Chebyshev-Legendre Transform Using an Asymptotic Formula

نویسندگان

  • Nicholas Hale
  • Alex Townsend
چکیده

A fast, simple, and numerically stable transform for converting between Legendre and Chebyshev coefficients of a degree N polynomial in O(N(logN)2/ log logN) 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 and numerical stability. Since the algorithm evaluates a Legendre expansion at an N +1 Chebyshev grid as an intermediate step, it also provides a fast transform between Legendre coefficients and values on a Chebyshev grid.

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عنوان ژورنال:
  • SIAM J. Scientific Computing

دوره 36  شماره 

صفحات  -

تاریخ انتشار 2014