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A block QR factorization algorithm for rank-deficient matrices

Conference ·
OSTI ID:6938041

This paper presents a new algorithm for computing the QR factorization of a rank-deficient matrix that is well suited for high-performance machines. These machines typically employ a memory hierarchy and matrix-matrix operations perform better on those machines than matrix-vector or vector-vector operations since they require significantly less data movement per floating point operation. The traditional QR factorization algorithm with column pivoting is not well suited for such environments since it precludes the use of matrix-matrix operations. Instead, we suggest a restricted pivoting strategy based on incremental condition estimation which allows us to formulate a block QR factorization algorithm where the bulk of the work is in matrix-matrix operations. Performance 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. 19 refs., 1 fig., 1 tab.

Research Organization:
Argonne National Lab., IL (USA)
Sponsoring Organization:
DOE/ER; NSF
DOE Contract Number:
W-31109-ENG-38
OSTI ID:
6938041
Report Number(s):
CONF-891273-4; ON: DE90010066; CNN: ASC-8715728
Country of Publication:
United States
Language:
English

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