The Application of the Fast Fourier Transform to Jacobi Polynomial expansions
نویسندگان
چکیده
We observe that the exact connection coefficient relations transforming modal coefficients of one Jacobi Polynomial class to the modal coefficients of certain other classes are sparse. Because of this, when one of the classes corresponds to the Chebyshev case, the Fast Fourier Transform can be used to quickly compute modal coefficients for Jacobi Polynomial expansions of class (α, β) when 2α and 2β are both odd integers. In addition, we present an algorithm for computing Jacobi spectral expansions that is more robust than Jacobi-Gauss quadrature. Numerical results are presented that illustrate the computational efficiency and accuracy advantage of our method over standard quadrature methods.
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