A New Algorithm For The Nonequispaced Fast Fourier Transform On The Rotation Group

We develop an approximate algorithm to efficiently calculate the discrete Fourier transform on the rotation group SO(3). Our method needs O(L-3 log L log(1/epsilon)+ log(3)(1/epsilon)Q) arithmetic operations for a degree-L transform at Q nodes free of choice and with desired accuracy epsilon. Our main contribution is a method that allows us to replace finite expansions in Wigner-d functions of arbitrary orders with those of low orders. It is based on new insights into the structure of related semiseparable matrices. This enables us to employ an established divide-and-conquer algorithm for symmetric semiseparable eigenproblems together with the fast multipole method to achieve an efficient algorithm.