  This paper presents new methodology for computationally efficient kernel
density estimation. It is shown that a large class of kernels allows for exact
evaluation of the density estimates using simple recursions. The same
methodology can be used to compute density derivative estimates exactly. Given
an ordered sample the computational complexity is linear in the sample size.
Combining the proposed methodology with existing approximation methods results
in extremely fast density estimation. Extensive experimentation documents the
effectiveness and efficiency of this approach compared with the existing
state-of-the-art.
