An Algorithm for the Rapid Evaluation of Special Function Transforms
YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE
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We introduce a fast algorithm for the numerical application to arbitrary vectors of several special function transforms. The algorithm requires On logn operations to apply to an arbitrary vector any n n matrix such that the rank of any p q contiguous submatrix is bounded by a constant times pqn. These rank bounds are proven here for the case of the Fourier-Bessel transform. Numerical experiments demonstrate a much wider applicability. The performance of the algorithm is illustrated via several numerical examples.
- Numerical Mathematics