Fast summation of functions on the rotation group (Q600861)

The authors present an algorithm to evaluate linear combinations of functions on the rotation group. The proposed approaches based on a nonequispaced fast Fourier transform on \(SO(3)\) take \(\mathcal{O}(M+N)\) arithmetic operations (complexity) for \(M\) and \(N\) arbitrarily distributed cource and targed nodes, respectively, the complexity \(\mathcal{O}(MN)\) of a classical algorithm being to large for the applications. An explicit theoretical error bounds, as well as numerical examples of the approximation errors are given. The proposed method is applied to the kernel density estimation from electron back scattering diffraction data, a problem relevant in texture analysis.