Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An a posteriori verification method for generalized real-symmetric
  eigenvalue problems in large-scale electronic state calculations   An a posteriori verification method is proposed for the generalized
real-symmetric eigenvalue problem and is applied to densely clustered
eigenvalue problems in large-scale electronic state calculations. The proposed
method is realized by a two-stage process in which the approximate solution is
computed by existing numerical libraries and is then verified in a moderate
computational time. The procedure returns intervals containing one exact
eigenvalue in each interval. Test calculations were carried out for organic
device materials, and the verification method confirms that all exact
eigenvalues are well separated in the obtained intervals. This verification
method will be integrated into EigenKernel (https://github.com/eigenkernel/),
which is middleware for various parallel solvers for the generalized eigenvalue
problem. Such an a posteriori verification method will be important in future
computational science.

26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
19
The categories of this paper are: eess