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         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2699c9caf6155e0598d9c980105b8118d/mhartmann",         
         "tags" : [
            "a-posteriori","decomposition,","dynamical","error","estimates,","kernel","methods,","model","nonlinear","offline/online","projection","reduction,","subspace","systems,","vorlaeufig"
         ],
         
         "intraHash" : "699c9caf6155e0598d9c980105b8118d",
         "interHash" : "e80ae72fe2c1f9f79f4f7f8f5ce00735",
         "label" : "Efficient a-posteriori error estimation for nonlinear kernel-based\n\treduced systems",
         "user" : "mhartmann",
         "description" : "",
         "date" : "2018-07-20 10:54:15",
         "changeDate" : "2018-07-20 08:54:15",
         "count" : 11,
         "pub-type": "article",
         "journal": "Systems and Control Letters",
         "year": "2012", 
         "url": "http://www.sciencedirect.com/science/article/pii/S0167691111002672", 
         
         "author": [ 
            "D. Wirtz","B. Haasdonk"
         ],
         "authors": [
         	
            	{"first" : "D.",	"last" : "Wirtz"},
            	{"first" : "B.",	"last" : "Haasdonk"}
         ],
         "volume": "61","number": "1","pages": "203 - 211","abstract": "In this paper, we consider the topic of model reduction for nonlinear\n\tdynamical systems based on kernel expansions. Our approach allows\n\tfor a full offline/online decomposition and efficient online computation\n\tof the reduced model. In particular, we derive an a-posteriori state-space\n\terror estimator for the reduction error. A key ingredient is a local\n\tLipschitz constant estimation that enables rigorous a-posteriori\n\terror estimation. The computation of the error estimator is realized\n\tby solving an auxiliary differential equation during online simulations.\n\tEstimation iterations can be performed that allow a balancing between\n\testimation sharpness and computation time. Numerical experiments\n\tdemonstrate the estimation improvement over different estimator versions\n\tand the rigor and effectiveness of the error bounds.",
         "file" : ":/home/dwirtz/dwirtzwww/WH10_preprint.pdf:PDF",
         
         "doi" : "10.1016/j.sysconle.2011.10.012",
         
         "bibtexKey": "wirtz2012efficient"

      }
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         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2c9ff784e6a0440b80b45055fa2c9df7e/mhartmann",         
         "tags" : [
            "a-posteriori","decomposition,","dynamical","error","estimates,","kernel","methods,","model","nonlinear","offline/online","parameterized","projection","reduction,","subspace","systems,","vorlaeufig"
         ],
         
         "intraHash" : "c9ff784e6a0440b80b45055fa2c9df7e",
         "interHash" : "e6dce191069323c30bda8a87cce2913a",
         "label" : "A-posteriori error estimation for parameterized kernel-based systems",
         "user" : "mhartmann",
         "description" : "",
         "date" : "2018-07-20 10:54:15",
         "changeDate" : "2018-07-20 08:54:15",
         "count" : 8,
         "pub-type": "inproceedings",
         "booktitle": "Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical\n\tModelling",
         "year": "2012", 
         "url": "http://www.ifac-papersonline.net/", 
         
         "author": [ 
            "Daniel Wirtz","Bernard Haasdonk"
         ],
         "authors": [
         	
            	{"first" : "Daniel",	"last" : "Wirtz"},
            	{"first" : "Bernard",	"last" : "Haasdonk"}
         ],
         "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.",
         "owner" : "haasdonk",
         
         "bibtexKey": "wirtz2012aposteriori"

      }
	  
   ]
}