Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The global extended-rational Arnoldi method for matrix function
  approximation   The numerical computation of matrix functions such as $f(A)V$, where $A$ is
an $n\times n$ large and sparse square matrix, $V$ is an $n \times p$ block
with $p\ll n$ and $f$ is a nonlinear matrix function, arises in various
applications such as network analysis ($f(t)=exp(t)$ or $f(t)=t^3)$, machine
learning $(f(t)=log(t))$, theory of quantum chromodynamics $(f(t)=t^{1/2})$,
electronic structure computation, and others. In this work, we propose the use
of global extended-rational Arnoldi method for computing approximations of such
expressions. The derived method projects the initial problem onto an global
extended-rational Krylov subspace
$\mathcal{RK}^{e}_m(A,V)=\text{span}(\{\prod\limits_{i=1}^m(A-s_iI_n)^{-1}V,\ldots,(A-s_1I_n)^{-1}V,V$
$,AV, \ldots,A^{m-1}V\})$ of a low dimension. An adaptive procedure for the
selection of shift parameters $\{s_1,\ldots,s_m\}$ is given. The proposed
method is also applied to solve parameter dependent systems. Numerical examples
are presented to show the performance of the global extended-rational Arnoldi
for these problems.

30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con