Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new estimate for a quantity involving the Chebyshev polynomials of the
  first kind   In this paper, we establish a new estimate (including lower and upper bounds)
for an important quantity involved in the convergence analysis of smoothed
aggregation algebraic multigrid methods. The new upper bound improves the
existing ones. And our upper bound is optimal.

32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg