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SIAM J. on Numerical Analysis / Volume 50 / Issue 1

SIAM J. Numer. Anal. 50, pp. 307-327 (21 pages)

On Rapid Computation of Expansions in Ultraspherical Polynomials

María José Cantero and Arieh Iserles

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We present an ${\cal O}(N\log_2N)$ 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 the discrete Fourier transform.

© 2012 Society for Industrial and Applied Mathematics

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KEYWORDS

AMS Subject Headings

42C10, 33C05, 65T50

PUBLICATION DATA

ISSN

0036-1429 (print)  
1095-7170 (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received April 04, 2011
Accepted November 11, 2011
Published online February 14, 2012
Digital Object Identifier
http://dx.doi.org/10.1137/110829568

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