Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Newton's method with deflation for isolated singularities of polynomial
  systems   We present a modification of Newton's method to restore quadratic convergence
for isolated singular solutions of polynomial systems. Our method is
symbolic-numeric: we produce a new polynomial system which has the original
multiple solution as a regular root. Using standard bases, a tool for the
symbolic computation of multiplicities, we show that the number of deflation
stages is bounded by the multiplicity of the isolated root. Our implementation
performs well on a large class of applications.

16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an