PUMA publications for /user/mathematik/methods,%20nonlinear%20parameterizedhttps://puma.ub.uni-stuttgart.de/user/mathematik/methods,%20nonlinear%20parameterizedPUMA RSS feed for /user/mathematik/methods,%20nonlinear%20parameterized2024-03-29T12:03:11+01:00A-posteriori error estimation for parameterized kernel-based systemshttps://puma.ub.uni-stuttgart.de/bibtex/2c9ff784e6a0440b80b45055fa2c9df7e/mathematikmathematik2018-07-20T10:54:37+02:00a-posteriori decomposition, dynamical error estimates, from:mhartmann ians kernel methods, model nonlinear offline/online parameterized projection reduction, subspace systems, vorlaeufig <span data-person-type="author" class="authorEditorList "><span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Daniel Wirtz" itemprop="url" href="/person/1e6dce191069323c30bda8a87cce2913a/author/0"><span itemprop="name">D. Wirtz</span></a></span>, </span> and <span><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Bernard Haasdonk" itemprop="url" href="/person/1e6dce191069323c30bda8a87cce2913a/author/1"><span itemprop="name">B. Haasdonk</span></a></span></span>. </span><span class="additional-entrytype-information"><span itemtype="http://schema.org/Book" itemscope="itemscope" itemprop="isPartOf"><em><span itemprop="name">Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical
Modelling</span>, </em></span>(<em><span>2012<meta content="2012" itemprop="datePublished"/></span></em>)</span>Fri Jul 20 10:54:37 CEST 2018Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical
ModellingA-posteriori error estimation for parameterized kernel-based systems2012a-posteriori decomposition, dynamical error estimates, from:mhartmann ians kernel methods, model nonlinear offline/online parameterized projection reduction, subspace systems, vorlaeufig This work is concerned with derivation of fully offine/online decomposable
effcient aposteriori error estimators for reduced parameterized nonlinear
kernel-based systems. The dynamical systems under consideration consist
of a nonlinear, time- and parameter-dependent kernel expansion representing
the system's inner dynamics as well as time- and parameter-affne
inputs, initial conditions and outputs. The estimators are established
for a reduction technique originally proposed in [7] and are an extension
of the estimators derived in [11] to the fully time-dependent, parameterized
setting. Key features for the effcient error estimation are to use
local Lipschitz constants provided by a certain class of kernels
and an iterative scheme to balance computation cost against estimation
sharpness. Together with the affnely time/parameter-dependent system
components a full offine/online decomposition for both the reduction
process and the error estimators is possible. Some experimental results
for synthetic systems illustrate the effcient evaluation of the derived
error estimators for different parameters.