  A fast multipole method (FMM) for asymptotically smooth kernel functions
(1/r, 1/r^4, Gauss and Stokes kernels, radial basis functions, etc.) based on a
Chebyshev interpolation scheme has been introduced in [Fong et al., 2009]. The
method has been extended to oscillatory kernels (e.g., Helmholtz kernel) in
[Messner et al., 2012]. Beside its generality this FMM turns out to be
favorable due to its easy implementation and its high performance based on
intensive use of highly optimized BLAS libraries. However, one of its
bottlenecks is the precomputation of the multiple-to-local (M2L) operator, and
its higher number of floating point operations (flops) compared to other FMM
formulations. Here, we present several optimizations for that operator, which
is known to be the costliest FMM operator. The most efficient ones do not only
reduce the precomputation time by a factor up to 340 but they also speed up the
matrix-vector product. We conclude with comparisons and numerical validations
of all presented optimizations.
