Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interval Enclosures of Upper Bounds of Roundoff Errors using
  Semidefinite Programming   A longstanding problem related to floating-point implementation of numerical
programs is to provide efficient yet precise analysis of output errors.
  We present a framework to compute lower bounds on largest absolute roundoff
errors, for a particular rounding model. This method applies to numerical
programs implementing polynomial functions with box constrained input
variables. Our study is based on three different hierarchies, relying
respectively on generalized eigenvalue problems, elementary computations and
semidefinite programming (SDP) relaxations. This is complementary of
over-approximation frameworks, consisting of obtaining upper bounds on the
largest absolute roundoff error. Combining the results of both frameworks
allows to get enclosures for upper bounds on roundoff errors.
  The under-approximation framework provided by the third hierarchy is based on
a new sequence of convergent robust SDP approximations for certain classes of
polynomial optimization problems. Each problem in this hierarchy can be solved
exactly via SDP. By using this hierarchy, one can provide a monotone
non-decreasing sequence of lower bounds converging to the absolute roundoff
error of a program implementing a polynomial function, applying for a
particular rounding model.
  We investigate the efficiency and precision of our method on non-trivial
polynomial programs coming from space control, optimization and computational
biology.

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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex