Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A non-iterative method for robustly computing the intersections between
  a line and a curve or surface   The need to compute the intersections between a line and a high-order curve
or surface arises in a large number of finite element applications. Such
intersection problems are easy to formulate but hard to solve robustly. We
introduce a non-iterative method for computing intersections by solving a
matrix singular value decomposition (SVD) and an eigenvalue problem. That is,
all intersection points and their parametric coordinates are determined in
one-shot using only standard linear algebra techniques available in most
software libraries. As a result, the introduced technique is far more robust
than the widely used Newton-Raphson iteration or its variants. The maximum size
of the considered matrices depends on the polynomial degree $q$ of the shape
functions and is $2q \times 3q$ for curves and $6 q^2 \times 8 q^2$ for
surfaces. The method has its origin in algebraic geometry and has here been
considerably simplified with a view to widely used high-order finite elements.
In addition, the method is derived from a purely linear algebra perspective
without resorting to algebraic geometry terminology. A complete implementation
is available from http://bitbucket.org/nitro-project/.

21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg