TR#: | CS0877 |

Class: | CS |

Title: | KRYLOV SUBSPACE METHODS FOR EIGENVALUES WITH SPECIAL PROPERTIES AND THEIR ANALYSIS FOR NORMAL MATRICES |

Authors: | Avram Sidi |

Not Available | |

Abstract: | In this paper we propose a general approach by which eigenvalues with a special property of a given matrix $A$ can be obtained. In this approach we first determine a scalar function $\psi:\C \rightarrow \C$ whose modulus ia maximized by the eigenvalues that have the special property. Next, we compute the generalized power iterations $u_{j+1} = \psi(A) u_j, j=0,1,...,$ where $u_0$ is an arbitrary initial vector. Finally, we apply known Krylov subspace methods, such as the methods of Arnoldi and Lanczos, to the vector $u_n$ for some sufficiently large $n$. We can also apply the simultaneous iteration method to the subspace span $\{x^{(n)}_1,..., x^{(n)}_k\}$ with some sufficiently large $n$, where $x^{(j+1)}_m = \psi(A) x^{(j)}_m,\ j = 0,1,..., m=1,...,k$. In all cases the resulting Ritz pairs are approximations to the eigenpairs of $A$ with the special property. We provide a pretty thorough convergence analysis of the approach involving all three methods as $n \rightarrow \infty$ for the case in which $A$ is a normal matrix. We also discuss the connections and similarities of our approach with the existing methods and approaches in the literature. |

Copyright | The above paper is copyright by the Technion, Author(s), or others. Please contact the author(s) for more information |

Remark: Any link to this technical report should be to this page (http://www.cs.technion.ac.il/users/wwwb/cgi-bin/tr-info.cgi/1996/CS/CS0877), rather than to the URL of the PDF files directly. The latter URLs may change without notice.

To the list of the CS technical reports of 1996

To the main CS technical reports page