Fast Summation of Functions on SO(3)
نویسندگان
چکیده
Computing with functions on SO(3) is a task found in various areas of application. When it comes to approximation kernel based methods are a suitable tool to handle these functions. In this paper we present an algorithm which allows us to evaluate linear combinations of functions on SO(3) as well as an truly fast algorithm to sum up radial functions on SO(3). These approaches based on non-equispaced FFTs on SO(3) take O(M + N) arithmetic operations for M and N arbitrarily distributed source and target nodes, respectively. We investigate a selection of radial functions and give explicit theoretical error bounds along with numerical examples on their approximation errors. Moreover we provide an application of our method, namely the kernel density estimation from electron back scattering diffraction (EBSD) data, a problem relevant in texture analysis.
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