Publications
Books
- 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.
Reprint Vieweg/Springer 2013 ISBN 978-3-322-93035-4.
E-Book ISBN 978-3-322-93034-7.
Selected papers
See also fulltext paper
- P. Mathé, B. Hofmann:
Tractability of linear ill-posed problems in Hilbert space.
Journal of Complexity 84 (2024), 101867,
https://doi.org/10.1016/j.jco.2024.101867. - S. Kindermann, B. Hofmann:
Curious ill-posedness phenomena in the composition of non-compact linear operators in Hilbert spaces.
Journal Inverse and Ill-Posed Problems 24 (2024), Number 5, 1001-1013,
https://doi.org/10.1515/jiip-2024-0007. - B. Hofmann, H.-J. Fischer:
A note on the degree of ill-posedness for mixed differentiation on the d-dimensional unit cube.
Journal Inverse and Ill-Posed Problems 23 (2023), Number 6, 949-957,
DOI: 10.1515/jiip-2023-0025. - O. Scherzer, B. Hofmann, Z. Nashed:
Gauss-Newton method for solving linear inverse problems with neural network coders.
Sampling theory, signal processing, and data analysis 21 (2023), Number 2, Article 25,
DOI: 10.1007/s43670-023-00066-6. - B. Hofmann, F. Werner, Y. Deng:
On uniqueness and ill-posedness for the deautoconvolution problem in the multi-dimensional case.
Inverse Problems 39 (2023), Number 6, 065012 (15pp),
DOI: 10.1088/1361-6420/acd07b. - B. Hofmann, C. Klinkhammer, R. Plato:
New results for variational regularization with oversmoothing penalty term in Banach spaces.
Communications on Analysis and Computation 1, Issue 2 (2023), 94-115,
DOI: 10.3934/cac.2023006. - Y. Deng, B. Hofmann, F. Werner:
Deautoconvolution in the two-dimensional case.
Electronic Transactions on Numerical Analysis 59 (2023), 24-42,
DOI: 10.1553/etna vol59s24. - B. Hofmann, P. Mathé:
The degree of ill-posedness of composite linear ill-posed problems with focus on the impact
of the non-compact Hausdorff moment operator.
Electronic Transactions on Numerical Analysis 57 (2022), 1-16.
DOI: 10.1553/etna vol57s1. - B. Hofmann, C. Hofmann, P. Mathé, R. Plato:
Nonlinear Tikhonov regularization in Hilbert scales with oversmoothing penalty: inspecting balancing principles.
Chapter 4 in: Deterministic and Stochastic Optimal Control and Inverse Problems (Eds.: B. Jadamba, A. A. Khan,
S. Migorski, M. Sama). CRC Press (Taylor & Francis Group), Boca Raton 2022, pp. 79-111.
ISBN 978-0-367-50630-8 (hbk), ISBN 978-0-367-50631-5 (pbk), ISBN 978-1-003-05057-5 (ebk),
DOI: 10.1201/9781003050575. - P. Mathé, M.T. Nair, B. Hofmann:
Regularization of linear ill-posed problems involving multiplication operators.
Applicable Analysis 101, Issue 2 (2022), 714-732,
DOI: 10.1080/00036811.2020.1758308. - D. Gerth, B. Hofmann:
A note on open questions asked to analysis and numerics concerning the Hausdorff moment problem.
Eurasian Journal of Mathematical and Computer Applications 10, Issue 1 (2022), 40-50. - D. Chen, B. Hofmann, I. Yousept:
Oversmoothing Tikhonov regularization in Banach spaces.
Inverse Problems 37 (2021), 085007 (28pp). - D. Gerth, B. Hofmann, C. Hofmann, S. Kindermann:
The Hausdorff moment problem in the light of ill-posedness of type I.
Eurasian Journal of Mathematical and Computer Applications 9, Issue 2 (2021), 57-87. - Y. Zhang, B. Hofmann:
Two new non-negativity preserving iterative regularization methods for ill-posed inverse problems.
Inverse Problems and Imaging 15 (2021), 229-256. - B. Hofmann, R.Plato:
Convergence results and low order rates for nonlinear Tikhonov regularization with oversmoothing penalty term.
Electronic Transactions on Numerical Analysis 53 (2020), 313-328. - F. Werner, B. Hofmann:
Convergence analysis of (statistical) inverse problems under conditional stability estimates.
Inverse Problems 36 (2020), 015004 (23pp). - Y. Zhang, B. Hofmann:
On the second-order asymptotical regularization of linear ill-posed problems.
Applicable Analysis 99 (2020), 1000-1025. - B. Hofmann, C. Hofmann:
The impact of the discrepancy principle on the Tikhonov-regularized solutions with oversmoothing penalties.
Mathematics (www.mdpi.com) 8 (2020), 331 (16pp). - B. Hofmann, P. Mathé:
A priori parameter choice in Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems.
Chapter 8 in: Inverse Problems and Related Topics: Shanghai, China, October 12-14, 2018
(Eds.: J. Cheng, S. Lu, M. Yamamoto). Book 310 of Springer Proceedings in Mathematics & Statistics. Springer Nature, Singapore 2020 (ISBN 978-981-15-1591-0. ISBN 978-981-15-1592-7 (eBook)), pp. 169-176. - D. Gerth, B. Hofmann, C. Hofmann:
Case studies and a pitfall for nonlinear variational regularization under conditional stability.
Chapter 9 in: Inverse Problems and Related Topics: Shanghai, China, October 12-14, 2018
(Eds.: J. Cheng, S. Lu, M. Yamamoto). Book 310 of Springer Proceedings in Mathematics & Statistics. Springer Nature, Singapore 2020 (ISBN 978-981-15-1591-0. ISBN 978-981-15-1592-7 (eBook)), pp. 177-203. - R. Gong, B. Hofmann, Y. Zhang:
A new class of accelerated regularization methods, with application to bioluminescence tomography.
Inverse Problems 36 (2020), 055013 (36pp). - R. Ramlau, C. Koutschan, B. Hofmann:
On the singular value decomposition of n-fold integration operators.
Chapter 11 in: Inverse Problems and Related Topics: Shanghai, China, October 12-14, 2018
(Eds.: J. Cheng, S. Lu, M. Yamamoto). Book 310 of Springer Proceedings in Mathematics & Statistics. Springer Nature, Singapore 2020 (ISBN 978-981-15-1591-0. ISBN 978-981-15-1592-7 (eBook)), pp. 237-256. - 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. - D. Gerth, B. Hofmann:
Oversmoothing regularization with l1-penalty term.
AIMS Mathematics 4 (2019), 1223-1247. - 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). - B. Hofmann, R. Plato:
On ill-posedness concepts, stable solvability and saturation
Journal of Inverse and Ill-posed Problems 26 (2018), 287-297. - 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.