Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Any admissible harmonic Ritz value set is possible for prescribed GMRES
  residual norms
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci