We first briefly report on the status and recent achievements of the ELPA-AEO<br />
(Eigenvalue Solvers for Petaflop Applications - Algorithmic Extensions and<br />
Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects.<br />
In both collaboratory efforts, scientists from the application areas,<br />
mathematicians, and computer scientists work together to develop and make<br />
available efficient highly parallel methods for the solution of eigenvalue<br />
problems. Then we focus on a topic addressed in both projects, the use of mixed<br />
precision computations to enhance efficiency. We give a more detailed<br />
description of our approaches for benefiting from either lower or higher<br />
precision in three selected contexts and of the results thus obtained.