  This paper introduces the R package FKSUM, which offers fast and exact
evaluation of univariate kernel smoothers. The main kernel computations are
implemented in C++, and are wrapped in simple, intuitive and versatile R
functions. The fast kernel computations are based on recursive expressions
involving the order statistics, which allows for exact evaluation of kernel
smoothers at all sample points in log-linear time. In addition to general
purpose kernel smoothing functions, the package offers purpose built and
ready-to-use implementations of popular kernel-type estimators. On top of these
basic smoothing problems, this paper focuses on projection pursuit problems in
which the projection index is based on kernel-type estimators of functionals of
the projected density.
