On Rapid Computation of Expansions in Ultraspherical Polynomials
نویسندگان
چکیده
We present an O(N log2 N) algorithm for the computation of the first N coefficients in the expansion of an analytic function in ultraspherical polynomials. We first represent expansion coefficients as an infinite linear combination of derivatives and then as an integral transform with a hypergeometric kernel along the boundary of a Bernstein ellipse. Following a transformation of the kernel, we approximate the coefficients to arbitrary accuracy using Discrete Fourier Transform.
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ورودعنوان ژورنال:
- SIAM J. Numerical Analysis
دوره 50 شماره
صفحات -
تاریخ انتشار 2012