## Abstract

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 language | English (US) |
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Pages (from-to) | 218-228 |

Number of pages | 11 |

Journal | Journal of Computational Physics |

Volume | 82 |

Issue number | 1 |

DOIs | |

State | Published - 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