  The problem of fast computation of multivariate kernel density estimation
(KDE) is still an open research problem. In our view, the existing solutions do
not resolve this matter in a satisfactory way. One of the most elegant and
efficient approach utilizes the fast Fourier transform. Unfortunately, the
existing FFT-based solution suffers from a serious limitation, as it can
accurately operate only with the constrained (i.e., diagonal) multivariate
bandwidth matrices. In this paper we describe the problem and give a
satisfactory solution. The proposed solution may be successfully used also in
other research problems, for example for the fast computation of the optimal
bandwidth for KDE.
