Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Any decreasing cycle-convergence curve is possible for restarted GMRES   Given a matrix order $n$, a restart parameter $m$ ($m < n$), a decreasing
positive sequence $f(0) > f(1) > ... > f(q) \geq 0$, where $q < n/m$, it is
shown that there exits an $n$-by-$n$ matrix $A$ and a vector $r_0$ with
$\|r_0\|=f(0)$ such that $\|r_k\|=f(k)$, $k=1,...,q$, where $r_k$ is the
residual at cycle $k$ of restarted GMRES with restart parameter $m$ applied to
the linear system $Ax=b$, with initial residual $r_0=b-Ax_0$. Moreover, the
matrix $A$ can be chosen to have any desired eigenvalues. We can also construct
arbitrary cases of stagnation; namely, when $f(0) > f(1) > ... > f(i) = f(i+1)
\geq 0 $ for any $i <q $. The restart parameter can be fixed or variable.

4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int