Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Solving a Generalized Chinese Remainder Theorem in the Presence of
  Remainder Errors   In estimating frequencies given that the signal waveforms are undersampled
multiple times, Xia et. al. proposed to use a generalized version of Chinese
remainder Theorem (CRT), where the moduli are $M_1, M_2, \cdots, M_k$ which are
not necessarily pairwise coprime. If the errors of the corrupted remainders are
within $\tau=\sds \max_{1\le i\le k} \min_{\stackrel{1\le j\le k}{j\neq i}}
\frac{\gcd(M_i,M_j)}4$, their schemes can be used to construct an approximation
of the solution to the generalized CRT with an error smaller than $\tau$.
Accurately finding the quotients is a critical ingredient in their approach. In
this paper, we shall start with a faithful historical account of the
generalized CRT. We then present two treatments of the problem of solving
generalized CRT with erroneous remainders. The first treatment follows the
route of Wang and Xia to find the quotients, but with a simplified process. The
second treatment considers a simplified model of generalized CRT and takes a
different approach by working on the corrupted remainders directly. This
approach also reveals some useful information about the remainders by
inspecting extreme values of the erroneous remainders modulo $4\tau$. Both of
our treatments produce efficient algorithms with essentially optimal
performance. Finally, this paper constructs a counterexample to prove the
sharpness of the error bound $\tau$.

10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat