New Software for Large Dense Symmetric Generalized Eigenvalue Problems Using Secondary Storage

摘要

Quantum mechanical bandstructure computations require repeated computation of a large number of eigenvalues of a symmetric generalized eigenproblem. In previous work of the authors the application of a block Lanczos algorithm, and a modification of the packed EISPACK routines, have been considered for the numerical solution of such eigenvalue problems arising in the theoretical calculation of pressure and volume at metallization of BaTe. Both approaches were limited in the size of problem, which could be handled by the existing software. The largest feasible problem for each method on a 4 Mword Cray X-MP/24 was about of the order of 1900. Here we report numerical results with some new software, which has been developed recently. This software permits the user to fully utilize a fast secondary storage device such as the SSD. On a 128 Mword SSD now the solution of generalized eigenvalue problems of order up to 8000 is feasible. In this note we give a brief summary of the new software and present some performance results and a comparison with other softwares.