A fully parallel method for the singular eigenvalue problem

Authors:
Kuiyuan Li;J. Uvah;Shengbian Zhao
Affiliations:
-;-;-
Venue:
Computers & Mathematics with Applications
Year:
2005

Citing 2
Cited 0

A fully parallel algorithm for the symmetric eigenvalue problem

SIAM Journal on Scientific and Statistical Computing
An algorithm for symmetric tridiagonal eigenproblems: divide and conquer with homotopy continuation

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	0.09

Visualization

Abstract

In this paper, a fully parallel method for finding some or all finite eigenvalues of a real symmetric matrix pencil (A, B) is presented, where A is a symmetric tridiagonal matrix and B is a diagonal matrix with b"1 0 and b"i = 0, i = 2,3,...,n. The method is based on the homotopy continuation with rank 2 perturbation. It is shown that there are exactly m disjoint, smooth homotopy paths connecting the trivial eigenvalues to the desired eigenvalues, where m is the number of finite eigenvalues of (A, B). It is also shown that the homotopy curves are monotonic and easy to follow.