PARALLEL SUBSPACE ITERATION METHOD FOR THE SPARSE SYMMETRIC EIGENVALUE PROBLEM

Author:

LOMBARDINI RICHARD1,POIRIER BILL1

Affiliation:

1. Department of Chemistry and Biochemistry, and Department of Physics, Texas Tech University, Box 41061, Lubbock, Texas 79409-1061, USA

Abstract

A new parallel iterative algorithm for the diagonalization of real sparse symmetric matrices is introduced, which uses a modified subspace iteration method. A novel feature is the preprocessing of the matrix prior to iteration, which allows for a natural parallelization resulting in a great speedup and scalability of the method with respect to the number of compute nodes. The method is applied to Hamiltonian matrices of model systems up to six degrees of freedom, represented in a truncated Weyl–Heisenberg wavelet (or "weylet") basis developed by one of the authors (Poirier). It is shown to accurately determine many thousands of eigenvalues for sparse matrices of the order N ≈ 106, though much larger matrices may also be considered.

Publisher

World Scientific Pub Co Pte Lt

Subject

Computational Theory and Mathematics,Physical and Theoretical Chemistry,Computer Science Applications

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