Time-memory trade-offs using sparse matrix methods for large-scale eigenvalue problems

  • Authors:

  • Keita Teranishi;Padma Raghavan;Chao Yang

  • Affiliations:

  • Department of Computer Science and Engineering, The Pennsylvania State University, University Park, PA;Department of Computer Science and Engineering, The Pennsylvania State University, University Park, PA;Lawrence Berkeley National Laboratory, Berkeley, CA

  • Venue:
  • ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
  • Year:
  • 2003

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Abstract

Iterative methods such as Lanczos and Jacobi-Davidson are typically used to compute a small number of eigenvalues and eigenvectors of a sparse matrix. However, these methods are not effective in certain large-scale applications, for example, "global tight binding molecular dynamics." Such applications require all the eigenvectors of a large sparse matrix; the eigenvectors can be computed a few at a time and discarded after a simple update step in the modeling process. We show that by using sparse matrix methods, a direct-iterative hybrid scheme can significantly reduce memory requirements while requiring less computational time than a banded direct scheme. Our method also allows a more scalable parallel formulation for eigenvector computation through spectrum slicing. We discuss our method and provide empirical results for a wide variety of sparse matrix test problems.