Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Condition Number Analysis of a Line-Surface Intersection Algorithm   We propose an algorithm based on Newton's method and subdivision for finding
all zeros of a polynomial system in a bounded region of the plane. This
algorithm can be used to find the intersections between a line and a surface,
which has applications in graphics and computer-aided geometric design. The
algorithm can operate on polynomials represented in any basis that satisfies a
few conditions. The power basis, the Bernstein basis, and the first-kind
Chebyshev basis are among those compatible with the algorithm. The main novelty
of our algorithm is an analysis showing that its running is bounded only in
terms of the condition number of the polynomial's zeros and a constant
depending on the polynomial basis.

9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin