Multidimensional Cooley-Tukey algorithms revisited (Q675881)

Based on the representation theory of finite Abelian groups, the authors derive fast multidimensional Fourier transform algorithms. For cyclic groups they obtain as special case the Cooley-Tukey and Good-Thomas algorithms. For groups with several generators they get a variety of multidimensional Cooley-Tukey type algorithms. They show that their approach results in data flow patterns which are different from the standard ``row-column'' approaches and demonstrate by a numerical example that in hierarchical memory environments these data flows are more efficient.