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Research Group Regularization



  • B. Hofmann, A. Leitao, J.P. Zubelli (Eds.):
    New Trends in Parameter Identification for Mathematical Models.
    Birkhäuser,Trends in Mathematics,
    Springer International Publishing, Cham, Switzerland 2018,
    ISBN 978-3-319-70823-2, ISBN 978-3-319-70824-9 (eBook)
  • T. Schuster, B. Kaltenbacher, B. Hofmann, K.S. Kazimierski:
    Regularization Methods in Banach Spaces.
    Walter de Gruyter GmbH & Co. KG,
    Reihe: Radon Series on Computational and Applied Mathematics 10,
    Berlin/Boston 2012, ISBN 978-3-11-025524-9.
  • B. Hofmann:
    Mathematik inverser Probleme.
    B.G. Teubner Stuttgart-Leipzig, Leipzig 1999.
    ISBN 978-3-519-00254-3. Fulltext download
  • B. Hofmann:
    Regularization for Applied Inverse and Ill-Posed Problems.
    B.G. Teubner Leipzig, Teubner-Texte zur Mathematik, Bd. 85, Leipzig 1986.

Selected papers

See also fulltext paper

  • Y. Zhang, B. Hofmann:
    On Fractional asymptotical regularization of linear ill-posed problems in Hilbert spaces.
    Fractional Calculus and Applied Analysis 22 (2019), 699-721.
  • E. Escoto, D. Gerth, B. Hofmann, G. Steinmeyer:
    Strategies for the characterization of partially coherent ultrashort pulses with dispersion scan.
    Journal of the Optical Society of America B 36 (2019), 2092-2098.
  • R. Plato, B. Hofmann:
    A regularized variational inequality approach for nonlinear monotone ill-posed problems.
    Journal of Optimization Theory 182 (2019), 525-539.
  • W. Wang, S. Lu, B. Hofmann, J. Cheng:
    Tikhonov regularization with l0-term complementing a convex penalty: l1-convergence under sparsity constraints.
    Journal of Inverse and Ill-posed Problems 27 (2019), 575-590.
  • C. Hofmann, B. Hofmann, A. Pichler:
    Simultaneous identification of volatility and interest rate functions -- a two parameter regularization approach.
    Electronic Transactions on Numerical Analysis 51 (2019), 99-117.
  • M. Hinze, B. Hofmann, Tran Nhan Tam Quyen:
    A regularization approach for an inverse source problem in elliüptic systems from single Cauchy data.
    Numerical Functional Analysis and Optimization 40 (2019), 1080-1112.
  • B. Hofmann, S. Kindermann, P. Mathé:
    Penalty-based smoothness conditions in convex variational regularization.
    Journal of Inverse and Ill-posed Problems 27 (2019), 283-300.
  • D. Gerth, E. Escoto, G. Steinmeyer, B. Hofmann:
    Regularized differential evolution for a blind phase retrieval problem in ultrashort laser pulse characteriztaion.
    Review of Scientific Instruments 90 (2019), 043116.
  • H. Egger, B. Hofmann:
    Tikhonov regularization in Hilbert scales under conditional stability assumptions.
    Inverse Problems 34 (2018),115015 (17pp).
  • D. Chen, B. Hofmann, J. Zou:
    Regularization and convergence for ill-posed backward evolution equations in Banach spaces.
    J. Differential Equations 265 (2018), 3533-3566.
  • J. Flemming, D. Gerth:
    Injectivity and weak*-to-weak continuity suffice for convergence rates in l^1-regularization.
    Journal of Inverse and Ill-posed Problems 26 (2018), 85-94.
  • R. Plato, P. Mathé, B. Hofmann:
    Optimal rates for Lavrentiev regularization with adjoint source conditions.
    Mathematics of Computation 87 (2018), 785-801.
  • B. Hofmann, P. Mathé:
    Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales.
    Inverse Problems 34 (2018), 015007 (14pp).
  • D. Gerth:
    Convergence rates for l1-regularization without the help of a variational inequality.
    Electronic Transactions on Numerical Analysis 47 (2017), 233-244.
  • D. Gerth, A. Hofinger, R. Ramlau:
    On the lifting of deterministic convergence rates for inverse problems with stochastic noise.
    Inverse Problems and Imaging 11 (2017), 663 - 687.
  • S. Bürger, P. Mathé:
    Discretized Lavrent'ev regularization for the autoconvolution equation.
    Applicable Analysis 96 (2017), 1618-1637.
  • D. Chen, B. Hofmann, J. Zou:
    Elastic-net regularization versus l1-regularization for linear inverse problems with quasi-sparse solutions.
    Inverse Problems 33 (2017), 015004 (17pp).
  • R. Bot, B. Hofmann:
    Conditional stability versus ill-posedness for operator equations with monotone operators in Hilbert space.
    Inverse Problems 32 (2016), 125003 (23pp).
  • B. Hofmann, B. Kaltenbacher, E. Resmerita:
    Lavrentiev's regularization method in Hilbert spaces revisited.
    Inverse Problems and Imaging 10 (2016), 741-764.
  • S. Bürger, J. Flemming, B. Hofmann:
    On complex-valued deautoconvolution of compactly supported functions with sparse Fourier representation.
    Inverse Problems 32 (2016), 104006 (12pp).
  • J. Flemming:
    Convergence rates for l1-regularization without injectivity-type assumptions.
    Inverse Problems 32 (2016), 095001 (19pp).
  • J. Flemming, B. Hofmann, I. Veselic:
    A unified approach to convergence rates for l1-regularization and lacking sparsity.
    Journal of Inverse and Ill-posed Problems 24 (2016), 139-148.
  • S.W. Anzengruber, S. Bürger, B. Hofmann, G.Steinmeyer:
    Variational regularization of complex deautoconvolution and phase retrieval in ultrashort laser pulse characterization.
    Inverse Problems 32, No.3 (2016), 035002 (27pp).
  • J. Flemming, B. Hofmann, I. Veselic:
    On l1- regularization in light of Nashed's ill-posedness concept.
    Computational Methods in Applied Mathematics 15 (2015), 279-289.
  • S. Bürger, J. Flemming:
    Deautoconvolution: A new decomposition approach versus TIGRA and local regularization.
    Journal of Inverse and Ill-posed Problems 23 (2015), 231-243.
  • B. Hofmann:
    On smoothness concepts in regularization for nonlinear inverse problems in Banach spaces.
    Chapter~8 in Mathematical and Computational Modeling: With Applications in Natural and Social Sciences,
    Engineering, and the Arts (Ed.: R.~Melnik).
    John Wiley, New Jersey 2015, pp.~192--221. ISBN 978-1-118-85398-6.
  • S. Birkholz, G. Steinmeyer, S. Koke, D. Gerth, S. Bürger, B. Hofmann:
    Phase retrieval via regularization in self-diffraction-based spectral interferometry.
    Journal of the Optical Society of America B 32, No.5 (2015), 983-992.
  • S. Bürger, B. Hofmann:
    About a deficit in low-order convergence rates on the example of autoconvolution.
    Applicable Analysis 94, No.3 (2015), 477-493.
  • S.W. Anzengruber, B. Hofmann, P. Mathé:
    Regularization properties of the sequential discrepancy principle for Tikhonov regularization in Banach spaces.
    Applicable Analysis 93, No.7 (2014), 1382-1499.
  • J. Cheng, B. Hofmann, S. Lu:
    The index function and Tikhonov regularization for ill-posed problems.
    Journal of Computational and Applied Mathematics 265 (2014), 110-119.
  • D. Gerth, B. Hofmann, S. Birkholz, S. Koke, G. Steinmeyer:
    Regularization of an autoconvolution problem in ultrashort laser pulse characterization.
    Inverse Problems in Science and Engineering 22, No.2 (2014), 245-266.
  • J. Flemming:
    Regularization of autoconvolution and other ill-posed quadratic equations by decomposition.
    Journal of Inverse and Ill-posed Problems 22 (2014), 551-567.
  • S.W. Anzengruber, B. Hofmann, R.Ramlau:
    On the interplay of basis smoothness and specific range conditions occurring in sparsity regularization.
    Inverse Problems 29 (2013), 125002 (21pp).
  • U.Tautenhahn, U.Hämarik, B. Hofmann, Y.Shao:
    Conditional stability estimates for ill-posed PDE problems by using interpolation.
    Numerical Functional Analysis and Optimization 34 (2013), 1370-1417.
  • M. Burger, J. Flemming, B.Hofmann:
    Convergence rates in l1-regularization if the sparsity assumption fails.
    Inverse Problems 29 (2013), 025013 (16pp).
  • R. Bot, B. Hofmann:
    The impact of a curious type of smoothness conditions on convergence rates in l1-regularization.
    Eurasian Journal of Mathematical and Computer Applications 1, No.1 (2013), 29-40.
  • R. Bot, B. Hofmann, P. Mathé:
    Regularizability of ill-posed problems and the modulus of continuity.
    Zeitschrift f. Analysis und ihre Anwendungen 32, No.3 (2013), 299-312.
  • J. Flemming:
    Variational smoothness assumptions in convergence rate theory - an overview.
    Journal of Inverse and Ill-posed Problems 21 (2013), 395-409.
  • S. Lu, J. Flemming:
    Convergence rate analysis of Tikhonov regularization for nonlinear ill-posed problems with noisy operators.
    Inverse Problems 28 (2012), 104003 (20 pp).
  • J. Flemming:
    Solution smoothness of ill-posed equations in Hilbert spaces: four concepts and their cross connections.
    Applicable Analysis 91 (2012), 1029-1044.
  • B. Hofmann, P. Mathé:
    Parameter choice in Banach space regularization under variational inequalities.
    Inverse Problems 28 (2012), 104006 (17pp).
  • B. Hofmann, P. Mathé:
    A note on the modulus of continuity for ill-posed problems in Hilbert space.
    Trudy Inst. Mat. i Mekh. UrO RAN 18, No.1 (2012), 34-41.
  • J. Flemming, B.Hofmann:
    Convergence rates in constrained Tikhonov regularization: equivalence of projected source conditions and variational inequalities.
    Inverse Problems 27 (2011), 085001 (11pp).
  • M. Hegland, B. Hofmann:
    Errors of regularisation under range inclusions using variable Hilbert scales.
    Inverse Problems and Imaging 5 (2011), 619-643.
  • J. Flemming, B.Hofmann, P.Mathé:
    Sharp converse results for the regularization error using distance functions.
    Inverse Problems 27 (2011), 025006 (18pp).
  • J. Flemming:
    Theory and examples of variational regularization with non-metric fitting functionals.
    Journal of Inverse and Ill-posed Problems 18 (2010), 677-699.
  • B. Hofmann, S. Kindermann:
    On the degree of ill-posedness for linear problems with non-compact operators.
    Methods and Applications of Analysis 17 (2010), 445-461.
  • R.I.Bot, B.Hofmann:
    An extension of the variational approach for obtaining convergence rates in regularization of nonlinear ill-posed problems.
    Journal of Integral Equations and Applications 22 (2010), 369-392.
  • B.Hofmann, M.Yamamoto:
    On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems.
    Applicable Analysis 89 (2010), 1705-1727.
  • A.Neubauer, T.Hein, B.Hofmann, S.Kindermann, U.Tautenhahn:
    Improved and extended results for enhanced convergence rates of Tikhonov regularization in Banach spaces.
    Applicable Analysis 89 (2010), 1729-1743.
  • J. Flemming, B.Hofmann:
    A new approach to source conditions in regularization with general residual term.
    Numer. Funct. Anal. Optimiz. 31 (2010), 254-284.
  • S.V. Pereverzev, B.Hofmann:
    Estimation of linear functionals from indirect noisy data without knowledge of the noise level.
    GEM - International Journal on Geomathematics 1 (2010), 121-131.
  • B. Kaltenbacher, B.Hofmann:
    Convergence rates for the iteratively regularized Gauss-Newton method in Banach spaces.
    Inverse Problems 26 (2010), 035007 (21pp).
  • B.Hofmann, P.Mathé, H.von Weizsäcker:
    Regularization in Hilbert space under unbounded operators and general source conditions.
    Inverse Problems 25 (2009), 115013 (15pp).
  • T.Hein, B.Hofmann:
    Approximate source conditions for nonlinear ill-posed problems -- chances and limitations.
    Inverse Problems 25 (2009), 035003 (16pp).
  • B.Hofmann, L.von Wolfersdorf:
    A new result on the singular value asymptotics of integration operators with weights.
    Journal of Integral Equations and Applications 21 (2009), 281-295.
  • B.Hofmann, P.Mathé, M.Schieck:
    Modulus of continuity for conditionally stable ill-posed problems in Hilbert space.
    J. Inv. Ill-posed Problems 16 (2008), 567-585.
  • P.Mathé, B.Hofmann:
    How general are general source conditions?
    Inverse Problems 24 (2008), 015009 (5pp).
  • P.Mathé, B.Hofmann:
    Direct and inverse results in variable Hilbert scales.
    Journal of Approximation Theory 154 (2008), 77-89.
  • L. von Wolfersdorf, B.Hofmann:
    A specific inverse problem for the Volterra convolution equation.
    Applicable Analysis 87 (2008), 59-81.
  • B.Hofmann, P.Mathé, S.V.Pereverzev:
    Regularization by projection: Approximation theoretic aspects and distance functions.
    J. Inverse and Ill-Posed Problems 15 (2007), 527-545.
  • B. Hofmann, P.Mathé:
    Analysis of profile functions for general linear regularization methods
    SIAM J. Numer. Anal. 45 (2007), 1122-1141.
  • B. Hofmann, B. Kaltenbacher, C. Pöschl, O. Scherzer:
    A convergence rates result in Banach spaces with non-smooth operators
    Inverse Problems 23 (2007), 987-1010.
  • B. Hofmann, M. Schieck, L. von Wolfersdorf:
    On the analysis of distance functions for linear ill-posed problems with an application to the integration operator in L^2
    J. Inv. Ill-Posed Problems 15 (2007), 83-98.
  • D. Düvelmeyer, B. Hofmann, M. Yamamoto:
    Range inclusions and approximate source conditions with general benchmark functions
    Numerical Functional Analysis and Optimization 28 (2007), 1245-1261.
  • T. Hein, B. Hofmann, A. Meyer, P.Steinhorst:
    Numerical analysis of a calibration problem for simulating electric fault arc tests
    Inverse Problems in Science and Engineering 15 (2007), 679-698.
  • D. Düvelmeyer, B. Hofmann:
    A multi-parameter regularization approach for estimating parameters in jump diffusion processes
    J. Inv. Ill-Posed Problems 14 (2006), 861-880.
  • B. Hofmann:
    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.
  • A. Böttcher, B. Hofmann, U. Tautenhahn, M. Yamamoto:
    Convergence rates for Tikhonov regularization from different kinds of smoothness conditions
    Applicable Analysis 85 (2006), 555-578.
  • H. Egger, T. Hein, B. Hofmann:
    On decoupling of volatility smile and term structure in inverse option pricing
    Inverse Problems 22 (2006), 1247-1259.
  • B. Hofmann, D. Düvelmeyer, K. Krumbiegel:
    Approximate source conditions in Tikhonov regularization - new analytical results and some numerical studies
    Mathematical Modelling and Analysis 11 (2006), 41-56.
  • B. Hofmann, L. von Wolfersdorf:
    On the determination of a density function by its autoconvolution coefficient
    Numerical Functional Analysis and Optimization 27 (2006), 357-375.
  • B. Hofmann, M. Yamamoto:
    Convergence rates for Tikhonov regularization based on range inclusions
    Inverse Problems 21 (2005), 850-820.
  • M. Freitag, B. Hofmann:
    Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems
    J. Inverse and Ill-Posed Problems 13 (2005), 123-148.
  • B. Hofmann, R. Krämer:
    On maximum entropy regularization for a specific inverse problem of option pricing
    J. Inverse and Ill-Posed Problems 13 (2005), 41-63.
  • B. Hofmann, L. v. Wolfersdorf:
    Some results and a conjecture on the degree of ill-posedness for integration operators with weights
    Inverse Problems 21 (2005), 427-433.
  • P. Steinhorst, B. Hofmann, A. Meyer, W. Weinelt:
    Gas temperature identification for the simulation of electric fault arc tests
    Proceedings of 5th International Conference on Inverse Problems in Engineering: Theory and Practice, Cambridge July 2005, Volume III (Ed.: D. Lesnic), Leeds University Press, Leeds UK 2005, S12/1-8.
  • D. Düvelmeyer, B. Hofmann:
    Ill-posedness of parameter estimation in jump diffusion processes
    Tagungsband zum Workshop Stochastische Analysis
    Bärenstein 2004 (Hrsg.: J. vom Scheidt), TU Chemnitz, 5-20.
  • T. Hein, B. Hofmann:
    On the nature of ill-posedness of an inverse problem arising in option pricing
    Inverse Problems 19 (2003), 1319-1338.
  • B. Hofmann, F. Thießen, V. Weber, R. Wunderlich:
    Vermögensaufteilung für die Altersvorsorge: Wie fundiert sind langfristige Allokationsregeln?
    Zeitschrift für Bankrecht und Bankwirtschaft (ZBB) 15 (2003), 261-276.
  • S. Pohl, B. Hofmann, R. Neubert, T. Otto, C. Radehaus:
    A regularization approach for the determination of remission curves.
    Inverse Problems in Engineering 9 (2001), 157-174.
  • B. Hofmann, G. Fleischer:
    Stability rates for linear ill-posed problems with compact and non-compact operators.
    Z. Anal. Anwendungen 18 (1999), 267-286.
  • B. Hofmann, O. Scherzer:
    Local ill-posedness and source conditions of operator equations in Hilbert spaces.
    Inverse Problems 14 (1998), 1189-1206.
  • B. Hofmann, U. Tautenhahn:
    On ill-posedness measures and space change in Sobolev scales.
    Z. Anal. Anwendungen 16 (1997), 979-1000.
  • B. Hofmann:
    On the degree of ill-posedness for nonlinear problems.
    J. Inv. Ill-Posed Problems 2 (1994), 61-76.