(Kaltenbacher)Parameter Identification

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1、lecturenotesonParameterIdentificationinPartialDifferentialEquationsUniversityofLinzWS2005/06BarbaraKaltenbacherContents1Introduction41.1.Someexamples.................................42Theelectricalimpedancetomographyproblem92.1.Theinverseproblem..........

2、....................102.2.TransformationtoaSchr¨odingerequation..................102.3.Completenessofproductsofharmonicfunctions...............122.4.CompletenessofproductsofalmostexponentialsolutionsoftheSchr¨odingerequation.............................

3、........142.5.IdentifiabilityfortheSchr¨odingerequation..................182.6.IdentifiabilityfortheEITproblem......................193AninversesourceproblemforaparabolicPDE203.1.Inversesourceproblem.............................213.2.Orthogonality........

4、..........................213.3.Monotonicityprinciples.............................223.4.Uniqueness...................................234AninversecoefficientproblemforahyperbolicPDE274.1.Theinverseproblem..............................294.2.FormulationasaV

5、olterraintegralequation..................304.3.Uniqueness...................................325Aninversescatteringproblem355.1.Theforwardproblem..............................365.2.TheInverseproblem..............................416Numericalsolutiontechni

6、ques:Operatorequationmethods456.1.Preliminaries:Regularizationmethodsforlinearproblems.........466.2.Tikhonovregularizationfornonlinearproblems...............506.3.NonlinearLandweberIteration.........................546.3.1.BasicConditions..............

7、..............546.3.2.ConvergenceoftheLandweberIteration...............552Contents36.4.IterativelyRegularizedGauss-NewtonMethod................586.4.1.Convergenceanalysiswithaprioristoppingrule...........597Numericalsolutiontechniques:Thefactorizationme

8、thodforEIT651.IntroductionAlargevarietyofnatural,industrial,socialandeconomicalphenomenacanbemodeledby(systemsof)partialdifferentialequations(PDEs).WhendoingsimulationsbasedonaPDEmodel,itisassumedthatallinvolvedparameters—suchasco