Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How Many Numerical Eigenvalues can We Trust?   When using finite element and finite difference methods to approximate
eigenvalues of $2m^{th}$-order elliptic problems, the number of reliable
numerical eigenvalues can be estimated in terms of the total degrees of freedom
$N$ in resulting discrete systems. The truth is worse than what we used to
believe in that the percentage of reliable eigenvalues decreases with an
increased $N$, even though the number of reliable eigenvalues increases with
$N$.

24
The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics