Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Direct QR factorizations for tall-and-skinny matrices in MapReduce
  architectures   The QR factorization and the SVD are two fundamental matrix decompositions
with applications throughout scientific computing and data analysis. For
matrices with many more rows than columns, so-called "tall-and-skinny
matrices," there is a numerically stable, efficient, communication-avoiding
algorithm for computing the QR factorization. It has been used in traditional
high performance computing and grid computing environments. For MapReduce
environments, existing methods to compute the QR decomposition use a
numerically unstable approach that relies on indirectly computing the Q factor.
In the best case, these methods require only two passes over the data. In this
paper, we describe how to compute a stable tall-and-skinny QR factorization on
a MapReduce architecture in only slightly more than 2 passes over the data. We
can compute the SVD with only a small change and no difference in performance.
We present a performance comparison between our new direct TSQR method, a
standard unstable implementation for MapReduce (Cholesky QR), and the classic
stable algorithm implemented for MapReduce (Householder QR). We find that our
new stable method has a large performance advantage over the Householder QR
method. This holds both in a theoretical performance model as well as in an
actual implementation.

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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th