Accession Number:

ADA255892

Title:

On Computing Accurate Singular Values and Eigenvalues of Acyclic Matrices

Descriptive Note:

Technical rept. 1 Oct 1991-31 Mar 1992

Corporate Author:

NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF MATHEMATICS

Personal Author(s):

Report Date:

1992-08-07

Pagination or Media Count:

16.0

Abstract:

It is known that small relative perturbations in the entries of a bidiagonal matrix only cause small relative perturbations in its singular values, independent of the values of the matrix entries. In this paper we show that a matrix has this property if and only if its associated bipartite graph is acyclic. We also show how to compute the singular values of such a matrix to high relative accuracy. The same algorithm can compute eigenvalues of symmetric acyclic matrices with tiny component-wise relative backward error. This class includes tridragonal matfices, arrow matrices, and exponentially many others.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE