# A note on the eigenvalues of a special class of matrices

Cuminato, J.A. and McKee, S.
(2010)
*A note on the eigenvalues of a special class of matrices.*
Journal of Computational and Applied Mathematics, 234 (9).
pp. 2724-2731.
ISSN 0377-0427

## Abstract

In the analysis of stability of a variant of the Crank-Nicolson (C-N) method for the heat equation on a staggered grid a class of non-symmetric matrices appear that have an interesting property: their eigenvalues are all real and lie within the unit circle. In this note we shall show how this class of matrices is derived from the C-N method and prove that their eigenvalues are inside [-1,1] for all values of m (the order of the matrix) and all values of a positive parameter @s, the stability parameter. As the order of the matrix is general, and the parameter @s lies on the positive real line this class of matrices turns out to be quite general and could be of interest as a test set for eigenvalue solvers, especially as examples of very large matrices.

Item type: | Article |
---|---|

ID code: | 28240 |

Keywords: | 65F15, Crank-Nicolson, Eigenvalues, Special matrices, Tridiagonal matrices, Mathematics, Computational Mathematics, Applied Mathematics |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Mrs Carolynne Westwood |

Date Deposited: | 14 Oct 2010 14:40 |

Last modified: | 27 Apr 2016 16:07 |

Related URLs: | |

URI: | http://strathprints.strath.ac.uk/id/eprint/28240 |