{"c9ff784e6a0440b80b45055fa2c9df7ebritsteiner":{"DOI":"","ISBN":"","ISSN":"","URL":"http://www.ifac-papersonline.net/","abstract":"This work is concerned with derivation of fully offine/online decomposable\n\teffcient aposteriori error estimators for reduced parameterized nonlinear\n\tkernel-based systems. The dynamical systems under consideration consist\n\tof a nonlinear, time- and parameter-dependent kernel expansion representing\n\tthe system's inner dynamics as well as time- and parameter-affne\n\tinputs, initial conditions and outputs. The estimators are established\n\tfor a reduction technique originally proposed in [7] and are an extension\n\tof the estimators derived in [11] to the fully time-dependent, parameterized\n\tsetting. Key features for the effcient error estimation are to use\n\tlocal Lipschitz constants provided by a certain class of kernels\n\tand an iterative scheme to balance computation cost against estimation\n\tsharpness. Together with the affnely time/parameter-dependent system\n\tcomponents a full offine/online decomposition for both the reduction\n\tprocess and the error estimators is possible. Some experimental results\n\tfor synthetic systems illustrate the effcient evaluation of the derived\n\terror estimators for different parameters.","annote":"","author":[{"family":"Wirtz","given":"Daniel"},{"family":"Haasdonk","given":"Bernard"}],"citation-label":"Wirtz2012a","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2012"]],"literal":"2012"},"event-place":"","id":"c9ff784e6a0440b80b45055fa2c9df7ebritsteiner","interhash":"e6dce191069323c30bda8a87cce2913a","intrahash":"c9ff784e6a0440b80b45055fa2c9df7e","issue":"","issued":{"date-parts":[["2012"]],"literal":"2012"},"keyword":"a-posteriori anm decomposition, dynamical error estimates, ians kernel methods, model nonlinear offline/online parameterized projection reduction, subspace systems,","misc":{"owner":"haasdonk","file":":PDF/WH12b_preprint.pdf:PDF","groups":"haasdonk, haasdonk_all_papers"},"note":"","number":"","page":"","page-first":"","publisher":"","publisher-place":"","status":"","title":"A-posteriori error estimation for parameterized kernel-based systems","type":"paper-conference","username":"britsteiner","version":"","volume":""},"c9ff784e6a0440b80b45055fa2c9df7emathematik":{"DOI":"","ISBN":"","ISSN":"","URL":"http://www.ifac-papersonline.net/","abstract":"This work is concerned with derivation of fully offine/online decomposable\n\teffcient aposteriori error estimators for reduced parameterized nonlinear\n\tkernel-based systems. The dynamical systems under consideration consist\n\tof a nonlinear, time- and parameter-dependent kernel expansion representing\n\tthe system's inner dynamics as well as time- and parameter-affne\n\tinputs, initial conditions and outputs. The estimators are established\n\tfor a reduction technique originally proposed in [7] and are an extension\n\tof the estimators derived in [11] to the fully time-dependent, parameterized\n\tsetting. Key features for the effcient error estimation are to use\n\tlocal Lipschitz constants provided by a certain class of kernels\n\tand an iterative scheme to balance computation cost against estimation\n\tsharpness. Together with the affnely time/parameter-dependent system\n\tcomponents a full offine/online decomposition for both the reduction\n\tprocess and the error estimators is possible. Some experimental results\n\tfor synthetic systems illustrate the effcient evaluation of the derived\n\terror estimators for different parameters.","annote":"","author":[{"family":"Wirtz","given":"Daniel"},{"family":"Haasdonk","given":"Bernard"}],"citation-label":"wirtz2012aposteriori","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical\n\tModelling","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2012"]],"literal":"2012"},"event-place":"","id":"c9ff784e6a0440b80b45055fa2c9df7emathematik","interhash":"e6dce191069323c30bda8a87cce2913a","intrahash":"c9ff784e6a0440b80b45055fa2c9df7e","issue":"","issued":{"date-parts":[["2012"]],"literal":"2012"},"keyword":"a-posteriori decomposition, dynamical error estimates, from:mhartmann ians kernel methods, model nonlinear offline/online parameterized projection reduction, subspace systems, vorlaeufig","misc":{"owner":"haasdonk"},"note":"","number":"","page":"","page-first":"","publisher":"","publisher-place":"","status":"","title":"A-posteriori error estimation for parameterized kernel-based systems","type":"paper-conference","username":"mathematik","version":"","volume":""},"c9ff784e6a0440b80b45055fa2c9df7emhartmann":{"DOI":"","ISBN":"","ISSN":"","URL":"http://www.ifac-papersonline.net/","abstract":"This work is concerned with derivation of fully offine/online decomposable\n\teffcient aposteriori error estimators for reduced parameterized nonlinear\n\tkernel-based systems. The dynamical systems under consideration consist\n\tof a nonlinear, time- and parameter-dependent kernel expansion representing\n\tthe system's inner dynamics as well as time- and parameter-affne\n\tinputs, initial conditions and outputs. The estimators are established\n\tfor a reduction technique originally proposed in [7] and are an extension\n\tof the estimators derived in [11] to the fully time-dependent, parameterized\n\tsetting. Key features for the effcient error estimation are to use\n\tlocal Lipschitz constants provided by a certain class of kernels\n\tand an iterative scheme to balance computation cost against estimation\n\tsharpness. Together with the affnely time/parameter-dependent system\n\tcomponents a full offine/online decomposition for both the reduction\n\tprocess and the error estimators is possible. Some experimental results\n\tfor synthetic systems illustrate the effcient evaluation of the derived\n\terror estimators for different parameters.","annote":"","author":[{"family":"Wirtz","given":"Daniel"},{"family":"Haasdonk","given":"Bernard"}],"citation-label":"wirtz2012aposteriori","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical\n\tModelling","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2012"]],"literal":"2012"},"event-place":"","id":"c9ff784e6a0440b80b45055fa2c9df7emhartmann","interhash":"e6dce191069323c30bda8a87cce2913a","intrahash":"c9ff784e6a0440b80b45055fa2c9df7e","issue":"","issued":{"date-parts":[["2012"]],"literal":"2012"},"keyword":"a-posteriori decomposition, dynamical error estimates, kernel methods, model nonlinear offline/online parameterized projection reduction, subspace systems, vorlaeufig","misc":{"owner":"haasdonk"},"note":"","number":"","page":"","page-first":"","publisher":"","publisher-place":"","status":"","title":"A-posteriori error estimation for parameterized kernel-based systems","type":"paper-conference","username":"mhartmann","version":"","volume":""}}