We develop an approximate algorithm to efficiently calculate the discrete Fourier transform on the rotation group SO(3). Our method needs O(L³ log L log (1/ε) + log³ (1/ε)\,Q) arithmetic operations for a degree-L transform at Q nodes free of choice and with desired accuracy ε. 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.
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Keiner et al. (2012) studied this question.
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