## Efficient parallel solution of sparse eigenvalue and eigenvector problems

Publication
, Journal Article

Reif, JH

Published in: Annual Symposium on Foundations of Computer Science - Proceedings

December 1, 1995

A new algorithm for computing the characteristic polynomial of a symmetric sparse matrix is given. An interesting algebraic version of Nested Dissection is derived, which constructs a sparse factorization of the matrix A - λI where A is the input matrix. While Nested Dissection is commonly used to minimize the fill-in in the solution of sparse linear systems, the innovation is to use the separator structure to bound also the work for manipulation of rational polynomials in the recursively factored matrices. The other innovation is an interesting reduction from finding all eigenvectors to the problems of back-solving a sparse linear system and multi-point polynomial evaluation.

### Duke Scholars

## Published In

Annual Symposium on Foundations of Computer Science - Proceedings

## ISSN

0272-5428

## Publication Date

December 1, 1995

## Start / End Page

123 / 132

### Citation

APA

Chicago

ICMJE

MLA

NLM

Reif, J. H. (1995). Efficient parallel solution of sparse eigenvalue and eigenvector problems.

*Annual Symposium on Foundations of Computer Science - Proceedings*, 123–132.Reif, J. H. “Efficient parallel solution of sparse eigenvalue and eigenvector problems.”

*Annual Symposium on Foundations of Computer Science - Proceedings*, December 1, 1995, 123–32.Reif JH. Efficient parallel solution of sparse eigenvalue and eigenvector problems. Annual Symposium on Foundations of Computer Science - Proceedings. 1995 Dec 1;123–32.

Reif, J. H. “Efficient parallel solution of sparse eigenvalue and eigenvector problems.”

*Annual Symposium on Foundations of Computer Science - Proceedings*, Dec. 1995, pp. 123–32.Reif JH. Efficient parallel solution of sparse eigenvalue and eigenvector problems. Annual Symposium on Foundations of Computer Science - Proceedings. 1995 Dec 1;123–132.

## Published In

Annual Symposium on Foundations of Computer Science - Proceedings

## ISSN

0272-5428

## Publication Date

December 1, 1995

## Start / End Page

123 / 132