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

A block QR factorization algorithm using restricted pivoting

Conference ·
DOI:https://doi.org/10.1145/76263.76290· OSTI ID:5587289
 [1]
  1. Argonne National Lab., IL (USA)

This paper presents a new algorithm for computing the QR factorization of a rank-deficient matrix on high-performance machines. The algorithm is based on the Householder QR factorization algorithm with column pivoting. The traditional pivoting strategy is not well suited for machines with a memory hierarchy since it precludes the use of matrix-matrix operations. However, matrix-matrix operations perform better on those machines than matrix-vector or vector-vector operations since they involve significantly less data movement per floating point operation. We suggest a restricted pivoting strategy which allows us to formulate a block QR factorization algorithm where the bulk of the work is in matrix-matrix operations. Incremental condition estimation is used to ensure the reliability of the restricted pivoting scheme. Implementation results on the Cray 2, Cray X-MP and Cray-Y-MP show that the new algorithm performs significantly better than the traditional scheme and can more than halve the cost of computing the QR factorization. 36 refs., 3 tabs.

Research Organization:
Argonne National Lab., IL (USA)
Sponsoring Organization:
DOE/ER; NSF
DOE Contract Number:
W-31109-ENG-38
OSTI ID:
5587289
Report Number(s):
CONF-891149-8; ON: DE90001921
Country of Publication:
United States
Language:
English