论文信息 - THE SCIENCE OF DERIVING STABILITY ANALYSES

THE SCIENCE OF DERIVING STABILITY ANALYSES

We introduce a methodology for obtaining inventories of error results for families of numerical dense linear algebra algorithms. The approach for deriving the analyses is goal-oriented, systematic, and layered. The presentation places the analysis side-by-side with the algorithm so that it is obvious where error is introduced, making it attractive for use in the classroom. Yet the approach is sufficiently powerful to support the analysis of more complex algorithms, such as blocked variants that attain high performance. We provide what we believe to be the first analysis of a practical blocked LU factorization. Contrary to popular belief, the bound on the error is tighter than that of the corresponding unblocked algorithm.

Robert A. van de Geijn | Paolo Bientinesi | R. V. D. Geijn | P. Bientinesi

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