科研之友
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摘要
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.
- 出版日期2012
