Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Designing LU-QR hybrid solvers for performance and stability   This paper introduces hybrid LU-QR al- gorithms for solving dense linear
systems of the form Ax = b. Throughout a matrix factorization, these al-
gorithms dynamically alternate LU with local pivoting and QR elimination steps,
based upon some robustness criterion. LU elimination steps can be very
efficiently parallelized, and are twice as cheap in terms of floating- point
operations, as QR steps. However, LU steps are not necessarily stable, while QR
steps are always stable. The hybrid algorithms execute a QR step when a
robustness criterion detects some risk for instability, and they execute an LU
step otherwise. Ideally, the choice between LU and QR steps must have a small
computational overhead and must provide a satisfactory level of stability with
as few QR steps as possible. In this paper, we introduce several robustness
criteria and we establish upper bounds on the growth factor of the norm of the
updated matrix incurred by each of these criteria. In addition, we describe the
implementation of the hybrid algorithms through an exten- sion of the PaRSEC
software to allow for dynamic choices during execution. Finally, we analyze
both stability and performance results compared to state-of-the-art linear
solvers on parallel distributed multicore platforms.

3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio