Natur der Inkorrektheit, approximative Quelldarstellung und adaptierte Regularisierungsmethoden bei Identifikationsproblemen

• Applicant: Professor Dr. Bernd Hofmann
• Subject Area: Mathematics
• Term: from 2006 to 2011
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 18961338

• Final Report Year: 2008

Final Report Abstract

No abstract available

Publications

• A multi-parameter regularization approach for estimating parameters in jump diffusion processes. J. Inv. Ill-Posed Problems 14 (2006), 861-880
  Düvelmeyer, D.; Hofmann, B.
  
• Approximate source conditions in Tikhonov regularization – new analytical results and some numerical studies. Mathematical Modelling and Analysis 11 (2006), 41-56
  Hofmann, B.; Düvelmeyer, D.; Krumbiegel, K.
  
• Approximate source conditions in Tikhonov-Phillips regularization and consequences for inverse problems with multiplication operators. Mathematical Methods in the Applied Sciences 29 (2006), 351-371
  Hofmann, B.
  
• On decoupling of volatility smile and term structure in inverse option pricing. Inverse Problems 22 (2006), 1247-1259
  Egger, H.; Hein, T.; Hofmann, B.
  
• On the determination of a density function by its autoconvolution coefficient. Numerical Functional Analysis and Optimization 27 (2006), 357-375
  Hofmann, B.; Wolfersdorf, L. von
  
• A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators. Inverse Problems 23 (2007), 987-1010
  Hofmann, B.; Kaltenbacher, B.; Pöschl, C.; Scherzer, O.
  
• Analysis of profile functions for general linear regularization methods. SIAM J. Numer. Anal. 45 (2007), 1122-1141
  Hofmann, B.; Mathé, P.
  
• Identification of material parameters in linear elasticity – some numerical results. Preprint CSC/07-09 TU Chemnitz, Fak. f. Mathematik, 2007
  Hein, T.; Meyer, M.
  
• Multi-parameter regularization - convergence and convergence rates results. Preprint 2007-17, TU Chemnitz, Fak. f. Mathematik, 2007
  Hein, T.
  
• Numerical analysis of a calibration problem for simulating electric fault arc tests. Inverse Problems in Science and Engineering 15 (2007), 679-698
  Hein, T.; Hofmann, B.; Meyer, A.; Steinhorst, P.
  
• On solving implicitly defined inverse problems by SQP-approaches. Preprint CSC/07-10, TU Chemnitz, Fak. f. Mathematik, 2007
  Hein, T.
  
• On the analysis of distance functions for linear ill-posed problems with an application to the integration operator in L2. J. Inverse and Ill-Posed Problems 15 (2007), 83-98
  Hofmann, B.; Schieck, M.; Wolfersdorf, L. von
  
• Range inclusions and approximate source conditions with general benchmark functions. Numerical Functional Analysis and Optimization 28 (2007), 1245-1261
  Düvelmeyer, D.; Hofmann, B.; Yamamoto, M.
  
• Regularization by projection: Approximation theoretic aspects and distance functions. J. Inv. Ill-Posed Problems 15 (2007), 527- 545
  Hofmann, B.; Mathé, P.; Pereverzev, S.V.
  
• Regularization of ill-posed problems in Banach spaces – approximative source conditions and convergence rates results. Preprint 2007-28, TU Chemnitz, Fak. f. Mathematik, 2007
  Hein, T.
  
• Simultane Identifikation voneinander unabhängiger Materialparameter – numerische Studien. Preprint CSC/07-05, TU Chemnitz, Fak. f. Mathematik, 2007
  Hein, T.; Meyer, M.
  
• How general are general source conditions? Inverse Problems 24 (2008), 015009 (5pp)
  Mathé, P.; Hofmann, B.