By Topic

Parallel QR algorithm for the complete eigensystem of symmetric matrices

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
R. M. S. Ralha ; Departamento de Matematica, Universidade do Minho, Braga, Portugal

We propose a parallel organization of the QR algorithm for computing the complete eigensystem of symmetric matrices. We developed Occam versions of standard sequential implementations of the QR algorithm: the procedure qr1 which computes only eigenvalues and qr2 for the computation of all eigenvalues and eigenvectors. The Occam procedure parqr2 is a parallel implementation of qr2 and was tested on a pipeline of 16 transputers. Although parqr2 could be used to compute the eigenvalues and eigenvectors of a symmetric tridiagonal matrix, it is best suited to be used in conjunction with a parallel algorithm for the reduction of a dense symmetric matrix to tridiagonal form where the orthogonal transformations are accumulated in an explicit way. In the practical tests parqr2 has proved to be efficient and we have carried out a simple analyses that appears to indicate that it is possible to use efficiently a number p of processors of the same order of magnitude of the size n of the matrix (p⩽n/6). This is an interesting result from the point of view of the scalability of our parallel algorithm

Published in:

Parallel and Distributed Processing, 1995. Proceedings. Euromicro Workshop on

Date of Conference:

25-27 Jan 1995