Automatic performance tuning for the multi-section with multiple eigenvalues method for symmetric tridiagonal eigenproblems

Abstract

We propose multisection for the multiple eigenvalues (MME) method for determining the eigenvalues of symmetric tridiagonal matrices. We also propose a method using runtime optimization, and show how to optimize its performance by dynamically selecting the implementation parameters. Performance results using a Hitachi SR8000 super-computer with eight processors per node yield (1) up to 6.3x speedup over a conventional multisection method, and (2) up to 1.47x speedup over a statically optimized MME method. © Springer-Verlag Berlin Heidelberg 2007.