A new iterative scheme for obtaining eigenvectors of large, real-symmetric matrices

Ramesh Natarajan, David Vanderbilt

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


A rapidly convergent block-iterative scheme for the computation of a few of the lowest eigenvalues and eigenvectors of a large dense real symmetric matrix is proposed. The method is especially applicable to matrix eigenvalue problems that arise from the discretization of self-adjoint partial differential equations. One such application to certain symmetric matrices that arise in solid-state band structure calculations is considered in detail. The most timeconsuming parts of the present algorithm are a matrix multiplication and a Gauss-Siedel relaxation step which are performed on each iteration. These two parts can, however, be very efficiently implemented on a vector or parallel processing computer.

Original languageEnglish (US)
Pages (from-to)218-228
Number of pages11
JournalJournal of Computational Physics
Issue number1
StatePublished - May 1989

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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