Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Model order reduction and sparse orthogonal expansions for random linear
  dynamical systems   We consider linear dynamical systems of ordinary differential equations or
differential algebraic equations. Physical parameters are substituted by random
variables for an uncertainty quantification. We expand the state variables as
well as a quantity of interest into an orthogonal system of basis functions,
which depend on the random variables. For example, polynomial chaos expansions
are applicable. The stochastic Galerkin method yields a larger linear dynamical
system, whose solution approximates the unknown coefficients in the expansions.
The Hardy norms of the transfer function provide information about the
input-output behaviour of the Galerkin system. We investigate two approaches to
construct a sparse representation of the quantity of interest, where just a low
number of coefficients is non-zero. Firstly, a standard basis is reduced by the
omission of basis functions, whose accompanying Hardy norms are relatively
small. Secondly, a projection-based model order reduction is applied to the
Galerkin system and allows for the definition of new basis functions as a
sparse representation. In both cases, we prove error bounds on the sparse
approximation with respect to Hardy norms. Numerical experiments are
demonstrated for a test example modelling a linear electric circuit.

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The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio