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
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