Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

On a block implementation of Hessenberg multishift QR iteration: LAPACK working note No. 8

Technical Report ·
OSTI ID:6524413

The usual QR algorithm for finding the eigenvalues of a Hessenberg matrix H is based on vector-vector operations, e.g., adding a multiple of one row to another. The opportunities for parallelism in such an algorithm are limited. In this report, we describe a reorganization of the QR algorithm to permit either matrix-vector or matrix-matrix operations to be performed, both of which yield more efficient implementations on vector and parallel machines. The ideal is to chase a k by k bulge rather than a 1 by 1 or 2 by 2 bulge as in the standard QR algorithm. We report our preliminary numerical experiments on the CONVEX C-1 and CYBER 205 vector machines. 15 refs., 2 figs., 5 tabs.

Research Organization:
Argonne National Lab., IL (USA)
DOE Contract Number:
W-31109-ENG-38
OSTI ID:
6524413
Report Number(s):
ANL/MCS-TM-127; ON: TI89006471
Country of Publication:
United States
Language:
English