Numerical Experiments with Symmetric Eigensolvers

This report describes and analyzes numerical experiments carried out with various symmetric eigensolvers in the context of the material science code Wien 97. Of particular interest are the performance improvements achieved with a new Level 3 eigensolver. The techniques which lead to a significant speed up are (1) sophisticated blocking in the tridiagonalization step, which leads to a twosweep algorithm, and (2) computing eigenvectors using inverse iteration on an appropriately chosen band matrix. The new Level 3 eigensolver improves the locality of data references and leads to performance improvements of up to 200 % (depending on hardware features and the problem size)