Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Newton's method in practice: finding all roots of polynomials of degree
  one million efficiently   We use Newton's method to find all roots of several polynomials in one
complex variable of degree up to and exceeding one million and show that the
method, applied to appropriately chosen starting points, can be turned into an
algorithm that can be applied routinely to find all roots without deflation and
with the inherent numerical stability of Newton's method.
  We specify an algorithm that provably terminates and finds all roots of any
polynomial of arbitrary degree, provided all roots are distinct and exact
computation is available. It is known that Newton's method is inherently
stable, so computing errors do not accumulate; we provide an exact bound on how
much numerical precision is sufficient.

31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int