Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximate Pythagoras Numbers   The Pythagoras number of a sum of squares is the shortest length among its
sums of squares representations. In many rings, for example real polynomial
rings in two or more variables, there exists no upper bound on the Pythagoras
number for all sums of squares.
  In this paper we study how Pythagoras numbers behave with respect to small
perturbations of elements. We show that these approximate Pythagoras numbers
are often significantly smaller than their exact versions, and allow for
(almost) dimension-independent upper bounds. Our results use low-rank
approximations for Gram matrices of sums of squares, and estimates for the
operator norm of the Gram map.

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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom