Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Krylov approximation of ODEs with polynomial parameterization   We propose a new numerical method to solve linear ordinary differential
equations of the type $\frac{\partial u}{\partial t}(t,\varepsilon) =
A(\varepsilon) \, u(t,\varepsilon)$, where
$A:\mathbb{C}\rightarrow\mathbb{C}^{n\times n}$ is a matrix polynomial with
large and sparse matrix coefficients. The algorithm computes an explicit
parameterization of approximations of $u(t,\varepsilon)$ such that
approximations for many different values of $\varepsilon$ and $t$ can be
obtained with a very small additional computational effort. The derivation of
the algorithm is based on a reformulation of the parameterization as a linear
parameter-free ordinary differential equation and on approximating the product
of the matrix exponential and a vector with a Krylov method. The Krylov
approximation is generated with Arnoldi's method and the structure of the
coefficient matrix turns out to have an independence on the truncation
parameter so that it can also be interpreted as Arnoldi's method applied to an
infinite dimensional matrix. We prove the superlinear convergence of the
algorithm and provide a posteriori error estimates to be used as termination
criteria. The behavior of the algorithm is illustrated with examples stemming
from spatial discretizations of partial differential equations.

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The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
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The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int