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.
%0 Conference Paper
%1 wirtz2013aposteriori
%A Wirtz, Daniel
%A Haasdonk, Bernard
%D 2013
%E Troch, Inge
%E Breitenecker, Felix
%I Curran
%K ians liste unibibliografie
%P 763-768
%T A-posteriori error estimation for parameterized kernel-based systems
%V 2
%X 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.
%@ 978-1-62748-328-5
@inproceedings{wirtz2013aposteriori,
abstract = {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.},
added-at = {2019-06-17T14:25:24.000+0200},
author = {Wirtz, Daniel and Haasdonk, Bernard},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/23c33d0802234fc1140aadec3cfc37b09/britsteiner},
editor = {Troch, Inge and Breitenecker, Felix},
eventdate = {2012-02-15/2012-02-17},
eventtitle = {7th Vienna International Conference on Mathematical Modelling, MATHMOD 2012},
interhash = {e4b6e7e2d826cf59823c6a997c444c1f},
intrahash = {3c33d0802234fc1140aadec3cfc37b09},
isbn = {978-1-62748-328-5},
keywords = {ians liste unibibliografie},
language = {eng},
location = {Red Hook, NY},
maintitle = {7th Vienna International Conference on Mathematical Modelling 2012},
pages = {763-768},
publisher = {Curran},
timestamp = {2019-06-17T12:34:15.000+0200},
title = {A-posteriori error estimation for parameterized kernel-based systems},
venue = {Vienna},
volume = 2,
year = 2013
}