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