Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A more direct and better variant of New Q-Newton's method Backtracking
  for m equations in m variables   In this paper we apply the ideas of New Q-Newton's method directly to a
system of equations, utilising the specialties of the cost function
$f=||F||^2$, where $F=(f_1,\ldots ,f_m)$.
  The first algorithm proposed here is a modification of Levenberg-Marquardt
algorithm, where we prove some new results on global convergence and avoidance
of saddle points.
  The second algorithm proposed here is a modification of New Q-Newton's method
Backtracking, where we use the operator $\nabla ^2f(x)+\delta ||F(x)||^{\tau}$
instead of $\nabla ^2f(x)+\delta ||\nabla f(x)||^{\tau}$. This new version is
more suitable than New Q-Newton's method Backtracking itself, while currently
has better avoidance of saddle points guarantee than Levenberg-Marquardt
algorithms.
  Also, a general scheme for second order methods for solving systems of
equations is proposed. We will also discuss a way to avoid that the limit of
the constructed sequence is a solution of $H(x)^{\intercal}F(x)=0$ but not of
$F(x)=0$.

7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an