TY - JOUR

T1 - Parallel subspace iteration method for the sparse symmetric eigenvalue problem

AU - Lombardini, Richard

AU - Poirier, Bill

N1 - Funding Information:
This work was supported by awards from The Welch Foundation (D-1523), Research Corporation, and the Office of Advanced Scientific Computing Research, Mathematical, Information, and Computational Sciences Division of the US Department of Energy, under contract DE-FG03-02ER25534. We gratefully acknowledge use of “Jazz”, a 350-node computing cluster operated by the Mathematics and Computer Science Division at Argonne National Laboratory as part of its Laboratory Computing Resource Center.

PY - 2006/12

Y1 - 2006/12

N2 - 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.

AB - 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.

KW - Matrix diagonalization

KW - Rovibrational spectroscopy

KW - Schrödinger equation

KW - Weylets

UR - http://www.scopus.com/inward/record.url?scp=33845955293&partnerID=8YFLogxK

U2 - 10.1142/S0219633606002738

DO - 10.1142/S0219633606002738

M3 - Article

AN - SCOPUS:33845955293

VL - 5

SP - 801

EP - 818

JO - Journal of Theoretical and Computational Chemistry

JF - Journal of Theoretical and Computational Chemistry

SN - 0219-6336

IS - 4

ER -