Parallel subspace iteration method for the sparse symmetric eigenvalue problem

Richard Lombardini, Bill Poirier

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageEnglish
Pages (from-to)801-818
Number of pages18
JournalJournal of Theoretical and Computational Chemistry
Volume5
Issue number4
DOIs
StatePublished - Dec 2006

Keywords

  • Matrix diagonalization
  • Rovibrational spectroscopy
  • Schrödinger equation
  • Weylets

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