  In this short paper, the authors report a new computational approach in the
context of Density Functional Theory (DFT). It is shown how it is possible to
speed up the self-consistent cycle (iteration) characterizing one of the most
well-known DFT implementations: FLAPW. Generating the Hamiltonian and overlap
matrices and solving the associated generalized eigenproblems $Ax = \lambda Bx$
constitute the two most time-consuming fractions of each iteration. Two
promising directions, implementing the new methodology, are presented that will
ultimately improve the performance of the generalized eigensolver and save
computational time.
