  Earlier this decade, the so-called FEAST algorithm was released for computing
the eigenvalues of a matrix in a given interval. Previously, rational filter
functions have been examined as a parameter of FEAST. In this thesis, we expand
on existing work with the following contributions: (i) Obtaining
well-performing rational filter functions via standard minimisation algorithms,
(ii) Obtaining constrained rational filter functions efficiently, and (iii)
Improving existing rational filter functions algorithmically. Using our new
rational filter functions, FEAST requires up to one quarter fewer iterations on
average compared to state-of-art rational filter functions.
