Toward an Automatically Tuned Dense Symmetric Eigensolver for Shared Memory Machines

Computation of eigenvalues and eigenvectors of a dense symmetric matrix is one of the most important problems in numerical linear algebra. In applications such as molecular orbital methods and first-principles molecular dynamics, eigensolution of matrices of order more than 10,000 is now needed. One of the approaches to solve such a large problem in practical time is to use symmetric multi-processors (SMPs). To exploit the potential high performance of SMP machines, one has to consider two issues, namely, (i) minimizing the number of inter-processor synchronizations and (ii) utilize the cache memory efficiently, thereby avoiding memory access conflict among the processors.