Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Communication-avoiding Cholesky-QR2 for rectangular matrices   Scalable QR factorization algorithms for solving least squares and eigenvalue
problems are critical given the increasing parallelism within modern machines.
We introduce a more general parallelization of the CholeskyQR2 algorithm and
show its effectiveness for a wide range of matrix sizes. Our algorithm executes
over a 3D processor grid, the dimensions of which can be tuned to trade-off
costs in synchronization, interprocessor communication, computational work, and
memory footprint. We implement this algorithm, yielding a code that can achieve
a factor of $\Theta(P^{1/6})$ less interprocessor communication on $P$
processors than any previous parallel QR implementation. Our performance study
on Intel Knights-Landing and Cray XE supercomputers demonstrates the
effectiveness of this CholeskyQR2 parallelization on a large number of nodes.
Specifically, relative to ScaLAPACK's QR, on 1024 nodes of Stampede2, our
CholeskyQR2 implementation is faster by 2.6x-3.3x in strong scaling tests and
by 1.1x-1.9x in weak scaling tests.

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The categories of this paper are: physics
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The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th