Reproducible Tall-Skinny QR

8 years 12 days ago

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—Reproducibility is the ability to obtain bitwise identical results from different runs of the same program on the same input data, regardless of the available computing resources, or how they are scheduled. Recently, techniques have been proposed to attain reproducibility for BLAS operations [1], [2], [5], all of which rely on reproducibly computing the ﬂoating-point sum and dot product. Nonetheless, a reproducible BLAS library does not automatically translate into a reproducible higher-level linear algebra library, especially when communication is optimized. For instance, for the QR factorization, conventional algorithms such as Householder transformation or Gram-Schmidt process can be used to reproducibly factorize a ﬂoating-point matrix by ﬁxing the highlevel order of computation, for example column-by-column from left to right, and by using reproducible versions of level1 BLAS operations such as dot product and 2-norm. In a massively parallel environment, those algorithms ...

Hong Diep Nguyen, James Demmel

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