Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A stochastic homotopy tracking algorithm for parametric systems of
  nonlinear equations   The homotopy continuation method has been widely used in solving parametric
systems of nonlinear equations. But it can be very expensive and inefficient
due to singularities during the tracking even though both start and end points
are non-singular. The current tracking algorithms focus on the adaptivity of
the stepsize by estimating the distance to the singularities but cannot avoid
these singularities during the tracking. We present a stochastic homotopy
tracking algorithm that perturbs the original parametric system randomly each
step to avoid the singularities. We then prove that the stochastic solution
path introduced by this new method is still closed to the original solution
path theoretically. Moreover, several homotopy examples have been tested to
show the efficiency of the stochastic homotopy tracking method.

14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas