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The Expansion in Ultraspherical Polynomials: a Simple Procedure for the Fast Computation of the Ultraspherical Coefficients by De Micheli, Enrico; Viano, Giovanni Alberto is a scholarly article available to read on EtoBox.

What is The Expansion in Ultraspherical Polynomials: a Simple Procedure for the Fast Computation of the Ultraspherical Coefficients about?

We present a simple and fast algorithm for the computation of the coefficients of the expansion of a function f(cos u) in ultraspherical (Gegenbauer) polynomials. We prove that these coefficients coincide with the Fourier coefficients of an Abel-type transform of the function f(cos u). This allows us to fully exploit the computational efficiency of the Fast Fourier Transform, computing the first N ultraspherical coefficients in just O (N log_2 N) operations.

Author

De Micheli, Enrico; Viano, Giovanni Alberto

Published

2011

Language

EN