Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automatic rational approximation and linearization of nonlinear
  eigenvalue problems   We present a method for solving nonlinear eigenvalue problems using rational
approximation. The method uses the AAA method by Nakatsukasa, S\`{e}te, and
Trefethen to approximate the nonlinear eigenvalue problem by a rational
eigenvalue problem and is embedded in the state space representation of a
rational polynomial by Su and Bai. The advantage of the method, compared to
related techniques such as NLEIGS and infinite Arnoldi, is the efficient
computation by an automatic procedure. In addition, a set-valued approach is
developed that allows building a low degree rational approximation of a
nonlinear eigenvalue problem. The method perfectly fits the framework of the
Compact rational Krylov methods (CORK and TS-CORK), allowing to efficiently
solve large scale nonlinear eigenvalue problems. Numerical examples show that
the presented framework is competitive with NLEIGS and usually produces smaller
linearizations with the same accuracy but with less effort for the user.

37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga