Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the uniform distribution of rational inputs with respect to condition
  numbers of Numerical Analysis   We show that rational data of bounded input length are uniformly distributed
with respect to condition numbers of numerical analysis. We deal both with
condition numbers of Linear Algebra and with condition numbers for systems of
multivariate polynomial equations. For instance, we show that for any $w>1$ and
for any $n\times n$ rational matrix $M$ of bit length $O(n^4\log n) + \log w$,
the condition number $k(M)$ satisfies $k(M) \leq w n^{5/2}$ with probability at
least $1-2w^{-1}$. Similar estimates are shown for the condition number
$\mu_{norm}$ of M. Shub and S. Smale when applied to systems of multivariate
homogeneous polynomial equations of bounded input length. Finally we apply
these techniques to show the probability distribution of the precision (number
of bits of the denominator) required to write down approximate zeros of affine
systems of multivariate polynomial equations of bounded input length.

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The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: atom-ph