A block QR factorization algorithm using restricted pivoting
- 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
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