## Abstract

In this paper, continuous methods are introduced to compute both the extreme and interior eigenvalues and their corresponding eigenvectors for real symmetric matrices. The main idea is to convert the extreme and interior eigenvalue problems into some optimization problems. Then a continuous method which includes both a merit function and an ordinary differential equation (ODE) is introduced for each resulting optimization problem. The convergence of each ODE solution is proved for any starting point. The limit of each ODE solution for any starting point is fully studied. Both the extreme and the interior eigenvalues and their corresponding eigenvectors can be easily obtained under a very mild condition. Promising numerical results are also presented.

Original language | English |
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Pages (from-to) | 31-51 |

Number of pages | 21 |

Journal | Linear Algebra and Its Applications |

Volume | 415 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 May 2006 |

## Scopus Subject Areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

## User-Defined Keywords

- Continuous method
- Eigenvalue
- Eigenvector