An adaptive blocking strategy for matrix factorizations

Conference · Mon Jan 01 04:00:00 EST 1990

DOI:https://doi.org/10.1007/3-540-53065-7_101· OSTI ID:6745432

Bischof, C H; Lacroute, P G

On most high-performance architectures, data movement is slow compared to floating-point (in particular, vector) performance. On these architectures block algorithms have been successful for matrix computations. By considering a matrix as a collection of submatrices (the so-called blocks) one naturally arrives at algorithms that require little data movement. The optimal blocking strategy, however, depends on the computing environment and on the problem parameters. Current approaches use fixed-width blocking strategies which are not optimal. This paper presents an adaptive blocking'' methodology for determining in a systematic manner an optimal blocking strategy for a uniprocessor machine. We demonstrate this technique on a block QR factorization routine on a uniprocessor. After generating timing models for the high-level kernels of the algorithm we can formulate the optimal blocking strategy in a recurrence relation that we can solve inexpensively with a dynamic programming technique. Experiments on one processor of a CRAY 2 show that in fact the resulting blocking strategy is as good as any fixed-width blocking strategy. So while we do not know the optimum fixed-width blocking strategy unless we re-run the same problem several times, adaptive blocking provides optimum performance in the very first run. 22 refs., 4 figs.

• Research Organization: Argonne National Lab., IL (USA)
• Sponsoring Organization: DOE/ER
• DOE Contract Number: W-31109-ENG-38
• OSTI ID: 6745432
• Report Number(s): CONF-900992-2; ON: DE90011108
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
FACTORIZATION
MATHEMATICAL LOGIC
MATRICES
OPTIMIZATION
PARALLEL PROCESSING
PERFORMANCE
PROGRAMMING