Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Probabilistic Analysis of the Power of Arithmetic Filters   The assumption of real-number arithmetic, which is at the basis of
conventional geometric algorithms, has been seriously challenged in recent
years, since digital computers do not exhibit such capability.
  A geometric predicate usually consists of evaluating the sign of some
algebraic expression. In most cases, rounded computations yield a reliable
result, but sometimes rounded arithmetic introduces errors which may invalidate
the algorithms. The rounded arithmetic may produce an incorrect result only if
the exact absolute value of the algebraic expression is smaller than some
(small) varepsilon, which represents the largest error that may arise in the
evaluation of the expression. The threshold varepsilon depends on the structure
of the expression and on the adopted computer arithmetic, assuming that the
input operands are error-free.
  A pair (arithmetic engine,threshold) is an "arithmetic filter". In this paper
we develop a general technique for assessing the efficacy of an arithmetic
filter. The analysis consists of evaluating both the threshold and the
probability of failure of the filter.
  To exemplify the approach, under the assumption that the input points be
chosen randomly in a unit ball or unit cube with uniform density, we analyze
the two important predicates "which-side" and "insphere". We show that the
probability that the absolute values of the corresponding determinants be no
larger than some positive value V, with emphasis on small V, is Theta(V) for
the which-side predicate, while for the insphere predicate it is Theta(V^(2/3))
in dimension 1, O(sqrt(V)) in dimension 2, and O(sqrt(V) ln(1/V)) in higher
dimensions. Constants are small, and are given in the paper.

19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an