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Author ID: hofmann.bernd Recent zbMATH articles by "Hofmann, Bernd"
Published as: Hofmann, Bernd; Hofmann, B.
External Links: MGP
all top 5

Co-Authors

32 single-authored
18 Mathé, Peter
7 Flemming, Jens
7 Plato, Robert
6 Gerth, Daniel
6 Kindermann, Stefan
5 Hofmann, Christopher
5 von Wolfersdorf, Lothar
5 Yamamoto, Masahiro
4 Boţ, Radu Ioan
4 Cheng, Jin
4 Düvelmeyer, Dana
4 Fleischer, Gunter
4 Hein, Torsten
4 Kaltenbacher, Barbara
4 Scherzer, Otmar
4 Tautenhahn, Ulrich
4 Zhang, Ye
3 Anzengruber, Stephan W.
3 Burger, Steven K.
3 Chen, Dehan
3 Friedrich, Volkmar
3 Kabanikhin, Sergeĭ Igorevich
3 Ramlau, Ronny
3 Yagola, Anatoliĭ Grigor’evich
2 Fischer, Hans-Jürgen
2 Gorenflo, Rudolf
2 Hasanoǧlu, Alemdar
2 Hein, Torsten
2 Lesnic, Daniel
2 Lu, Shuai
2 Nashed, Zuhair
2 Neubauer, Andreas
2 Pereverzev, Sergei V.
2 Resmerita, Elena
2 Romanov, Vladimir Gavrilovich
2 Schachtzabel, Hartmut
2 Schieck, M.
2 Steinmeyer, Günter
2 Vasin, Vladimir Vasil’evich
2 Veselić, Ivan
2 Zou, Jun
1 Andreev, Vladimir B.
1 Anikonov, Yuriĭ Evgenievich
1 Banks, Harvey Thomas
1 Birkholz, Simon
1 Böttcher, Albrecht
1 Braunß, Hans-Andreas
1 Burger, Martin
1 Đinh Nho Hào
1 Dulikravich, George Stevo
1 Egger, Herbert
1 Engl, Heinz W.
1 Gellrich, Carsten
1 Gong, Rongfang
1 Hämarik, Uno
1 Hausding, Reiner
1 Hegland, Markus
1 Hinneberg, Hans-Jürgen
1 Kazimierski, Kamil S.
1 Koke, Sebastian
1 Koutschan, Christoph
1 Krumbiegel, Klaus
1 Kuchuk, Fikri J.
1 Meyer, Arnd
1 Nair, M. Thamban
1 Nashed, M. Zuhair
1 Petschmann, Jan-Frederik
1 Pichler, Alois
1 Pickalov, Valery V.
1 Pöschl, Christiane
1 Sacks, Paul E.
1 Schröter, Torsten
1 Schuster, Thomas
1 Shao, Yuanyuan
1 Shishlenin, Maxim Aleksandrovich
1 Slodička, Marián
1 Steinhorst, Peter
1 Tichatschke, Rainer
1 Triggiani, Roberto
1 Unger, Roman
1 von Weizsäcker, Heinrich
1 Wang, Wei
1 Wang, Yanfei
1 Yousept, Irwin
1 Zeisel, Helmut
1 Zirilli, Francesco
all top 5

Serials

28 Inverse Problems
14 Journal of Inverse and Ill-Posed Problems
8 Applicable Analysis
6 Zeitschrift für Analysis und ihre Anwendungen
5 ETNA. Electronic Transactions on Numerical Analysis
4 Wissenschaftliche Zeitschrift der Technischen Hochschule Karl-Marx-Stadt
4 Numerical Functional Analysis and Optimization
4 Optimization
3 Journal of Integral Equations and Applications
3 Inverse Problems and Imaging
3 Beiträge zur Numerischen Mathematik
2 Mathematical Methods in the Applied Sciences
2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
2 Computing
2 Inverse Problems in Science and Engineering
2 PAMM. Proceedings in Applied Mathematics and Mechanics
1 Indian Journal of Pure & Applied Mathematics
1 Rheologica Acta
1 Wissenschaftliche Zeitschrift der Technischen Universität Karl-Marx-Stadt
1 Mathematics of Computation
1 BIT
1 Journal of Approximation Theory
1 Journal of Computational and Applied Mathematics
1 Journal of Differential Equations
1 Journal of Optimization Theory and Applications
1 Mathematische Operationsforschung und Statistik. Series Optimization
1 Mathematische Operationsforschung und Statistik. Series Statistics
1 Numerische Mathematik
1 SIAM Journal on Numerical Analysis
1 Wissenschaftliche Zeitschrift. Mathematisch-Naturwissenschaftliche Fakultät
1 International Journal of Computer Mathematics
1 SIAM Journal on Mathematical Analysis
1 U.S.S.R. Computational Mathematics and Mathematical Physics
1 Methods and Applications of Analysis
1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
1 Fractional Calculus & Applied Analysis
1 Mathematical Modelling and Analysis
1 Computational Methods in Applied Mathematics
1 Teubner-Texte zur Mathematik
1 Radon Series on Computational and Applied Mathematics
1 GEM - International Journal on Geomathematics
1 Nonlinear Analysis. Theory, Methods & Applications
1 AIMS Mathematics
1 Sampling Theory, Signal Processing, and Data Analysis

Publications by Year

Citations contained in zbMATH Open

102 Publications have been cited 1,352 times in 644 Documents Cited by Year
Regularization methods in Banach spaces. Zbl 1259.65087
Schuster, Thomas; Kaltenbacher, Barbara; Hofmann, Bernd; Kazimierski, Kamil S.
195
2012
A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators. Zbl 1131.65046
Hofmann, B.; Kaltenbacher, B.; Pöschl, C.; Scherzer, O.
150
2007
Regularization for applied inverse and ill-posed problems. A numerical approach. Zbl 0606.65038
Hofmann, Bernd
56
1986
Analysis of profile functions for general linear regularization methods. Zbl 1137.47063
Hofmann, Bernd; Mathé, Peter
40
2007
How general are general source conditions? Zbl 1140.47006
Mathé, Peter; Hofmann, Bernd
39
2008
Factors influencing the ill-posedness of nonlinear problems. Zbl 0809.35157
Hofmann, Bernd; Scherzer, Otmar
35
1994
On autoconvolution and regularization. Zbl 0804.45003
Gorenflo, Rudolf; Hofmann, Bernd
34
1994
Convergence rates for the iteratively regularized Gauss-Newton method in Banach spaces. Zbl 1204.65060
Kaltenbacher, Barbara; Hofmann, Bernd
30
2010
Parameter choice in Banach space regularization under variational inequalities. Zbl 1253.47041
Hofmann, Bernd; Mathé, Peter
30
2012
Approximate source conditions in Tikhonov–Phillips regularization and consequences for inverse problems with multiplication operators. Zbl 1094.47015
Hofmann, Bernd
28
2006
On the nature of ill-posedness of an inverse problem arising in option pricing. Zbl 1086.91028
Hein, Torsten; Hofmann, Bernd
28
2003
An extension of the variational inequality approach for obtaining convergence rates in regularization of nonlinear ill-posed problems. Zbl 1206.47060
Boţ, Radu Ioan; Hofmann, Bernd
26
2010
On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems. Zbl 1207.47065
Hofmann, Bernd; Yamamoto, Masahiro
25
2010
Convergence rates in \(\ell^1\)-regularization if the sparsity assumption fails. Zbl 1262.49010
Burger, Martin; Flemming, Jens; Hofmann, Bernd
24
2013
On decoupling of volatility smile and term structure in inverse option pricing. Zbl 1112.91032
Egger, Herbert; Hein, Torsten; Hofmann, Bernd
24
2006
Regularization properties of the sequential discrepancy principle for Tikhonov regularization in Banach spaces. Zbl 1300.65031
Anzengruber, Stephan W.; Hofmann, Bernd; Mathé, Peter
23
2014
Convergence rates for Tikhonov regularization from different kinds of smoothness conditions. Zbl 1110.65041
Böttcher, Albrecht; Hofmann, Bernd; Tautenhahn, Ulrich; Yamamoto, Masahiro
23
2006
Approximate source conditions for nonlinear ill-posed problems-chances and limitations. Zbl 1233.47054
Hein, Torsten; Hofmann, Bernd
22
2009
A new approach to source conditions in regularization with general residual term. Zbl 1195.47040
Flemming, Jens; Hofmann, Bernd
21
2010
On the second-order asymptotical regularization of linear ill-posed inverse problems. Zbl 1443.47014
Zhang, Y.; Hofmann, B.
21
2020
Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales. Zbl 1396.65097
Hofmann, Bernd; Mathé, Peter
19
2018
Improved and extended results for enhanced convergence rates of Tikhonov regularization in Banach spaces. Zbl 1214.65031
Neubauer, Andreas; Hein, Torsten; Hofmann, Bernd; Kindermann, Stefan; Tautenhahn, Ulrich
18
2010
Sharp converse results for the regularization error using distance functions. Zbl 1229.65091
Flemming, Jens; Hofmann, Bernd; Mathé, Peter
17
2011
Regularization of an autoconvolution problem in ultrashort laser pulse characterization. Zbl 1304.47013
Gerth, Daniel; Hofmann, Bernd; Birkholz, Simon; Koke, Sebastian; Steinmeyer, Günter
14
2014
About a deficit in low-order convergence rates on the example of autoconvolution. Zbl 1312.65087
Bürger, Steven; Hofmann, Bernd
14
2015
Modulus of continuity for conditionally stable ill-posed problems in Hilbert space. Zbl 1156.47013
Hofmann, B.; Mathé, P.; Schieck, M.
14
2008
Lavrentiev’s regularization method in Hilbert spaces revisited. Zbl 1348.65091
Hofmann, Bernd; Kaltenbacher, Barbara; Resmerita, Elena
13
2016
Conditional stability estimates for ill-posed PDE problems by using interpolation. Zbl 1280.35168
Tautenhahn, U.; Hämarik, U.; Hofmann, B.; Shao, Y.
13
2013
Elastic-net regularization versus \(\ell^{1}\)-regularization for linear inverse problems with quasi-sparse solutions. Zbl 06701168
Chen, De-Han; Hofmann, Bernd; Zou, Jun
13
2017
Local ill-posedness and source conditions of operator equations in Hilbert spaces. Zbl 0915.65052
Hofmann, Bernd; Scherzer, Otmar
13
1998
On the degree of ill-posedness for nonlinear problems. Zbl 0818.35137
Hofmann, B.
13
1994
On inversion rates for the autoconvolution equation. Zbl 0862.45007
Fleischer, Gunter; Hofmann, Bernd
12
1996
Convergence analysis of (statistical) inverse problems under conditional stability estimates. Zbl 1485.65059
Werner, Frank; Hofmann, Bernd
12
2020
On maximum entropy regularization for a specific inverse problem of option pricing. Zbl 1086.91029
Hofmann, B.; Krämer, R.
12
2005
Convergence rates for Tikhonov regularization based on range inclusions. Zbl 1077.65056
Hofmann, Bernd; Yamamoto, Masahiro
12
2005
On fractional asymptotical regularization of linear ill-posed problems in Hilbert spaces. Zbl 1478.65059
Zhang, Ye; Hofmann, Bernd
11
2019
On the interplay of basis smoothness and specific range conditions occurring in sparsity regularization. Zbl 1292.65056
Anzengruber, Stephan W.; Hofmann, Bernd; Ramlau, Ronny
11
2013
Range inclusions and approximate source conditions with general benchmark functions. Zbl 1136.47008
Düvelmeyer, Dana; Hofmann, Bernd; Yamamoto, Masahiro
10
2007
Regularization by projection: approximation theoretic aspects and distance functions. Zbl 1134.65039
Hofmann, B.; Mathé, P.; Pereverzev, S. V.
10
2007
A new class of accelerated regularization methods, with application to bioluminescence tomography. Zbl 07371378
Gong, Rongfang; Hofmann, Bernd; Zhang, Ye
9
2020
Variational regularization of complex deautoconvolution and phase retrieval in ultrashort laser pulse characterization. Zbl 1342.78045
Anzengruber, Stephan W.; Bürger, Steven; Hofmann, Bernd; Steinmeyer, Günter
8
2016
The index function and Tikhonov regularization for ill-posed problems. Zbl 1293.65086
Cheng, Jin; Hofmann, Bernd; Lu, Shuai
8
2014
Some results and a conjecture on the degree of ill-posedness for integration operators with weights. Zbl 1080.47015
Hofmann, Bernd; von Wolfersdorf, Lothar
8
2005
A unified approach to convergence rates for \(\ell^{1}\)-regularization and lacking sparsity. Zbl 1336.65104
Flemming, Jens; Hofmann, Bernd; Veselić, Ivan
7
2016
On complex-valued deautoconvolution of compactly supported functions with sparse Fourier representation. Zbl 1431.47005
Bürger, Steven; Flemming, Jens; Hofmann, Bernd
7
2016
Regularization in Hilbert space under unbounded operators and general source conditions. Zbl 1178.47006
Hofmann, Bernd; Mathé, Peter; von Weizsäcker, Heinrich
7
2009
A multi-parameter regularization approach for estimating parameters in jump diffusion processes. Zbl 1105.62103
Düvelmeyer, D.; Hofmann, B.
7
2006
Direct and inverse results in variable Hilbert scales. Zbl 1169.41003
Mathé, Peter; Hofmann, Bernd
7
2008
Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems. Zbl 1083.65054
Freitag, M.; Hofmann, B.
7
2005
Convergence rates in constrained Tikhonov regularization: equivalence of projected source conditions and variational inequalities. Zbl 1233.47053
Flemming, Jens; Hofmann, Bernd
7
2011
Regularization and convergence for ill-posed backward evolution equations in Banach spaces. Zbl 06901111
Chen, De-Han; Hofmann, Bernd; Zou, Jun
6
2018
Optimal rates for Lavrentiev regularization with adjoint source conditions. Zbl 1380.65096
Plato, Robert; Mathé, Peter; Hofmann, Bernd
6
2018
Mathematics of inverse problems. (Mathematik inverser Probleme.) Zbl 0942.45004
Hofmann, Bernd
6
1999
On \(\ell^1\)-regularization in light of Nashed’s ill-posedness concept. Zbl 1319.47006
Flemming, Jens; Hofmann, Bernd; Veselić, Ivan
5
2015
Optimization aspects of the generalized discrepancy principle in regularization. Zbl 0592.65021
Hofmann, B.
5
1986
On the analysis of distance functions for linear ill-posed problems with an application to the integration operator in \(L^2\). Zbl 1123.47014
Hofmann, B.; Schieck, M.; von Wolfersdorf, L.
5
2007
On the determination of a density function by its autoconvolution coefficient. Zbl 1099.47049
Hofmann, Bernd; von Wolfersdorf, Lothar
5
2006
Convergence results and low-order rates for nonlinear Tikhonov regularization with oversmoothing penalty term. Zbl 07192776
Hofmann, Bernd; Plato, Robert
5
2020
On the degree of ill-posedness for linear problems with noncompact operators. Zbl 1228.47017
Hofmann, Bernd; Kindermann, Stefan
5
2010
A study of regularization by monotonicity. Zbl 0774.65099
Gellrich, C.; Hofmann, B.
5
1993
Ill-posedness and local ill-posedness concepts in Hilbert spaces. Zbl 0981.65072
Hofmann, Bernd
4
2000
Conditional stability versus ill-posedness for operator equations with monotone operators in Hilbert space. Zbl 1368.47044
Boţ, Radu Ioan; Hofmann, Bernd
4
2016
On ill-posedness measures and space change in Sobolev scales. Zbl 0896.65043
Hofmann, B.; Tautenhahn, U.
4
1997
Penalty-based smoothness conditions in convex variational regularization. Zbl 1483.65087
Hofmann, Bernd; Kindermann, Stefan; Mathé, Peter
4
2019
Tikhonov regularization with \({\ell^{0}}\)-term complementing a convex penalty: \({\ell^{1}}\)-convergence under sparsity constraints. Zbl 1480.65139
Wang, Wei; Lu, Shuai; Hofmann, Bernd; Cheng, Jin
4
2019
On the autoconvolution equation and total variation constraints. Zbl 0923.65098
Fleischer, G.; Gorenflo, R.; Hofmann, B.
4
1999
Regularizability of ill-posed problems and the modulus of continuity. Zbl 1288.47015
Boţ, Radu Ioan; Hofmann, Bernd; Mathé, Peter
4
2013
A specific inverse problem for the Volterra convolution equation. Zbl 1148.45014
von Wolfersdorf, Lothar; Hofmann, Bernd
4
2008
Oversmoothing regularization with \(\ell^1\)-penalty term. Zbl 1484.47021
Gerth, Daniel; Hofmann, Bernd
4
2019
Approximate source conditions in Tikhonov regularization – new analytical results and some numerical studies. Zbl 1110.65043
Hofmann, B.; Düvelmeyer, D.; Krumbiegel, K.
3
2006
A priori parameter choice in Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems. Zbl 1437.65048
Hofmann, Bernd; Mathé, Peter
3
2020
On a class of ill-posed nonlinear integral equations arising in the interpretation of indirect measurements. Zbl 0742.65100
Hofmann, Bernd
3
1991
Oversmoothing Tikhonov regularization in Banach spaces. Zbl 1483.65086
Chen, De-Han; Hofmann, Bernd; Yousept, Irwin
3
2021
Uniqueness of monotone solutions to a non-linear Fredholm integral equation. Zbl 0733.45008
Hofmann, B.; Schachtzabel, H.
3
1991
Regularization methods for ill-posed problems. Zbl 1259.65086
Cheng, Jin; Hofmann, Bernd
3
2011
Well-posed and ill-posed situations in option pricing problems when the volatility is purely time-dependent. Zbl 1354.91149
Hofmann, Bernd; Hein, Torsten
2
2003
Regularization methods for ill-posed problems. 2nd edition. Zbl 1331.65081
Cheng, Jin; Hofmann, Bernd
2
2015
A predictor-corrector technique for constrained least-squares regularization. Zbl 0616.65062
Friedrich, Volkmar; Hofmann, Bernd
2
1987
A decreasing rearrangement approach for a class of ill-posed nonlinear integral equations. Zbl 0799.65149
Engl, Heinz W.; Hofmann, Bernd; Zeisel, Helmut
2
1993
Two new non-negativity preserving iterative regularization methods for ill-posed inverse problems. Zbl 1520.47029
Zhang, Ye; Hofmann, Bernd
2
2021
Case studies and a pitfall for nonlinear variational regularization under conditional stability. Zbl 1443.65080
Gerth, Daniel; Hofmann, Bernd; Hofmann, Christopher
2
2020
A new result in the singular value asymptotics of integration operators with weights. Zbl 1167.45303
Hofmann, Bernd; Von Wolfersdorf, Lothar
2
2009
Approximation of the inverse electrical impedance tomography problem by an inverse transmission problem. Zbl 0992.78020
Hofmann, B.
2
1998
Stability rates for linear ill-posed problems with compact and non-compact operators. Zbl 0941.65055
Hofmann, B.; Fleischer, G.
2
1999
Regularization of a Volterra integral equation by linear inequalities. Zbl 0697.65095
Hofmann, B.; Hausding, R.; Wolke, R.
2
1990
Errors of regularisation under range inclusions using variable Hilbert scales. Zbl 1252.47009
Hegland, Markus; Hofmann, Bernd
2
2011
Simultaneous identification of volatility and interest rate functions – a two-parameter regularization approach. Zbl 07099939
Hofmann, Christopher; Hofmann, Bernd; Pichler, Alois
1
2019
The local degree of ill-posedness and the autoconvolution equation. Zbl 0894.47048
Fleischer, Gunter; Hofmann, Bernd
1
1997
Decomposition cases of nonlinear ill-posed problems. Zbl 0886.47035
Hofmann, B.; Schröter, T.
1
1996
Regularization of nonlinear problems and the degree of ill-posedness. Zbl 0812.47065
Hofmann, Bernd
1
1993
Über Quelldarstellungen bei einigen linearen Regularisierungsverfahren. Zbl 0399.65038
Hofmann, Bernd
1
1979
Die Methode der Quasiinversion als Regularisierungsverfahren im Hilbertraum. Zbl 0457.65040
Hofmann, Bernd
1
1981
On the singular value decomposition of \(n\)-fold integration operators. Zbl 1512.47020
Ramlau, Ronny; Koutschan, Christoph; Hofmann, Bernd
1
2020
Deautoconvolution in the two-dimensional case. Zbl 07693762
Deng, Yu; Hofmann, Bernd; Werner, Frank
1
2023
Zur Regularisierung nichtlinearer inverser Probleme. Zbl 0512.65048
Hofmann, Bernd
1
1982
On the quasi-solution of overdetermined ill-conditioned systems of linear equations and its realization by means of parametric linear programming. Zbl 0515.90066
Tichatschke, R.; Hofmann, B.
1
1980
The degree of ill-posedness of composite linear ill-posed problems with focus on the impact of the non-compact Hausdorff moment operator. Zbl 07538268
Hofmann, Bernd; Mathé, Peter
1
2022
Nonlinear Tikhonov regularization in Hilbert scales with oversmoothing penalty: inspecting balancing principles. Zbl 1523.65046
Hofmann, Bernd; Hofmann, Christopher; Mathé, Peter; Plato, Robert
1
2022
Ill-posedness and regularization of inverse problem – a review of mathematical methods. Zbl 0923.35205
Hofmann, Bernd
1
1995
A denseness theorem with an application to a two-dimensional inverse potential refraction problem. Zbl 0937.35183
Hofmann, Bernd
1
1999
Deautoconvolution in the two-dimensional case. Zbl 07693762
Deng, Yu; Hofmann, Bernd; Werner, Frank
1
2023
The degree of ill-posedness of composite linear ill-posed problems with focus on the impact of the non-compact Hausdorff moment operator. Zbl 07538268
Hofmann, Bernd; Mathé, Peter
1
2022
Nonlinear Tikhonov regularization in Hilbert scales with oversmoothing penalty: inspecting balancing principles. Zbl 1523.65046
Hofmann, Bernd; Hofmann, Christopher; Mathé, Peter; Plato, Robert
1
2022
Oversmoothing Tikhonov regularization in Banach spaces. Zbl 1483.65086
Chen, De-Han; Hofmann, Bernd; Yousept, Irwin
3
2021
Two new non-negativity preserving iterative regularization methods for ill-posed inverse problems. Zbl 1520.47029
Zhang, Ye; Hofmann, Bernd
2
2021
On the second-order asymptotical regularization of linear ill-posed inverse problems. Zbl 1443.47014
Zhang, Y.; Hofmann, B.
21
2020
Convergence analysis of (statistical) inverse problems under conditional stability estimates. Zbl 1485.65059
Werner, Frank; Hofmann, Bernd
12
2020
A new class of accelerated regularization methods, with application to bioluminescence tomography. Zbl 07371378
Gong, Rongfang; Hofmann, Bernd; Zhang, Ye
9
2020
Convergence results and low-order rates for nonlinear Tikhonov regularization with oversmoothing penalty term. Zbl 07192776
Hofmann, Bernd; Plato, Robert
5
2020
A priori parameter choice in Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems. Zbl 1437.65048
Hofmann, Bernd; Mathé, Peter
3
2020
Case studies and a pitfall for nonlinear variational regularization under conditional stability. Zbl 1443.65080
Gerth, Daniel; Hofmann, Bernd; Hofmann, Christopher
2
2020
On the singular value decomposition of \(n\)-fold integration operators. Zbl 1512.47020
Ramlau, Ronny; Koutschan, Christoph; Hofmann, Bernd
1
2020
On fractional asymptotical regularization of linear ill-posed problems in Hilbert spaces. Zbl 1478.65059
Zhang, Ye; Hofmann, Bernd
11
2019
Penalty-based smoothness conditions in convex variational regularization. Zbl 1483.65087
Hofmann, Bernd; Kindermann, Stefan; Mathé, Peter
4
2019
Tikhonov regularization with \({\ell^{0}}\)-term complementing a convex penalty: \({\ell^{1}}\)-convergence under sparsity constraints. Zbl 1480.65139
Wang, Wei; Lu, Shuai; Hofmann, Bernd; Cheng, Jin
4
2019
Oversmoothing regularization with \(\ell^1\)-penalty term. Zbl 1484.47021
Gerth, Daniel; Hofmann, Bernd
4
2019
Simultaneous identification of volatility and interest rate functions – a two-parameter regularization approach. Zbl 07099939
Hofmann, Christopher; Hofmann, Bernd; Pichler, Alois
1
2019
Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales. Zbl 1396.65097
Hofmann, Bernd; Mathé, Peter
19
2018
Regularization and convergence for ill-posed backward evolution equations in Banach spaces. Zbl 06901111
Chen, De-Han; Hofmann, Bernd; Zou, Jun
6
2018
Optimal rates for Lavrentiev regularization with adjoint source conditions. Zbl 1380.65096
Plato, Robert; Mathé, Peter; Hofmann, Bernd
6
2018
Elastic-net regularization versus \(\ell^{1}\)-regularization for linear inverse problems with quasi-sparse solutions. Zbl 06701168
Chen, De-Han; Hofmann, Bernd; Zou, Jun
13
2017
Lavrentiev’s regularization method in Hilbert spaces revisited. Zbl 1348.65091
Hofmann, Bernd; Kaltenbacher, Barbara; Resmerita, Elena
13
2016
Variational regularization of complex deautoconvolution and phase retrieval in ultrashort laser pulse characterization. Zbl 1342.78045
Anzengruber, Stephan W.; Bürger, Steven; Hofmann, Bernd; Steinmeyer, Günter
8
2016
A unified approach to convergence rates for \(\ell^{1}\)-regularization and lacking sparsity. Zbl 1336.65104
Flemming, Jens; Hofmann, Bernd; Veselić, Ivan
7
2016
On complex-valued deautoconvolution of compactly supported functions with sparse Fourier representation. Zbl 1431.47005
Bürger, Steven; Flemming, Jens; Hofmann, Bernd
7
2016
Conditional stability versus ill-posedness for operator equations with monotone operators in Hilbert space. Zbl 1368.47044
Boţ, Radu Ioan; Hofmann, Bernd
4
2016
About a deficit in low-order convergence rates on the example of autoconvolution. Zbl 1312.65087
Bürger, Steven; Hofmann, Bernd
14
2015
On \(\ell^1\)-regularization in light of Nashed’s ill-posedness concept. Zbl 1319.47006
Flemming, Jens; Hofmann, Bernd; Veselić, Ivan
5
2015
Regularization methods for ill-posed problems. 2nd edition. Zbl 1331.65081
Cheng, Jin; Hofmann, Bernd
2
2015
Regularization properties of the sequential discrepancy principle for Tikhonov regularization in Banach spaces. Zbl 1300.65031
Anzengruber, Stephan W.; Hofmann, Bernd; Mathé, Peter
23
2014
Regularization of an autoconvolution problem in ultrashort laser pulse characterization. Zbl 1304.47013
Gerth, Daniel; Hofmann, Bernd; Birkholz, Simon; Koke, Sebastian; Steinmeyer, Günter
14
2014
The index function and Tikhonov regularization for ill-posed problems. Zbl 1293.65086
Cheng, Jin; Hofmann, Bernd; Lu, Shuai
8
2014
Convergence rates in \(\ell^1\)-regularization if the sparsity assumption fails. Zbl 1262.49010
Burger, Martin; Flemming, Jens; Hofmann, Bernd
24
2013
Conditional stability estimates for ill-posed PDE problems by using interpolation. Zbl 1280.35168
Tautenhahn, U.; Hämarik, U.; Hofmann, B.; Shao, Y.
13
2013
On the interplay of basis smoothness and specific range conditions occurring in sparsity regularization. Zbl 1292.65056
Anzengruber, Stephan W.; Hofmann, Bernd; Ramlau, Ronny
11
2013
Regularizability of ill-posed problems and the modulus of continuity. Zbl 1288.47015
Boţ, Radu Ioan; Hofmann, Bernd; Mathé, Peter
4
2013
Regularization methods in Banach spaces. Zbl 1259.65087
Schuster, Thomas; Kaltenbacher, Barbara; Hofmann, Bernd; Kazimierski, Kamil S.
195
2012
Parameter choice in Banach space regularization under variational inequalities. Zbl 1253.47041
Hofmann, Bernd; Mathé, Peter
30
2012
Sharp converse results for the regularization error using distance functions. Zbl 1229.65091
Flemming, Jens; Hofmann, Bernd; Mathé, Peter
17
2011
Convergence rates in constrained Tikhonov regularization: equivalence of projected source conditions and variational inequalities. Zbl 1233.47053
Flemming, Jens; Hofmann, Bernd
7
2011
Regularization methods for ill-posed problems. Zbl 1259.65086
Cheng, Jin; Hofmann, Bernd
3
2011
Errors of regularisation under range inclusions using variable Hilbert scales. Zbl 1252.47009
Hegland, Markus; Hofmann, Bernd
2
2011
Convergence rates for the iteratively regularized Gauss-Newton method in Banach spaces. Zbl 1204.65060
Kaltenbacher, Barbara; Hofmann, Bernd
30
2010
An extension of the variational inequality approach for obtaining convergence rates in regularization of nonlinear ill-posed problems. Zbl 1206.47060
Boţ, Radu Ioan; Hofmann, Bernd
26
2010
On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems. Zbl 1207.47065
Hofmann, Bernd; Yamamoto, Masahiro
25
2010
A new approach to source conditions in regularization with general residual term. Zbl 1195.47040
Flemming, Jens; Hofmann, Bernd
21
2010
Improved and extended results for enhanced convergence rates of Tikhonov regularization in Banach spaces. Zbl 1214.65031
Neubauer, Andreas; Hein, Torsten; Hofmann, Bernd; Kindermann, Stefan; Tautenhahn, Ulrich
18
2010
On the degree of ill-posedness for linear problems with noncompact operators. Zbl 1228.47017
Hofmann, Bernd; Kindermann, Stefan
5
2010
Approximate source conditions for nonlinear ill-posed problems-chances and limitations. Zbl 1233.47054
Hein, Torsten; Hofmann, Bernd
22
2009
Regularization in Hilbert space under unbounded operators and general source conditions. Zbl 1178.47006
Hofmann, Bernd; Mathé, Peter; von Weizsäcker, Heinrich
7
2009
A new result in the singular value asymptotics of integration operators with weights. Zbl 1167.45303
Hofmann, Bernd; Von Wolfersdorf, Lothar
2
2009
How general are general source conditions? Zbl 1140.47006
Mathé, Peter; Hofmann, Bernd
39
2008
Modulus of continuity for conditionally stable ill-posed problems in Hilbert space. Zbl 1156.47013
Hofmann, B.; Mathé, P.; Schieck, M.
14
2008
Direct and inverse results in variable Hilbert scales. Zbl 1169.41003
Mathé, Peter; Hofmann, Bernd
7
2008
A specific inverse problem for the Volterra convolution equation. Zbl 1148.45014
von Wolfersdorf, Lothar; Hofmann, Bernd
4
2008
A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators. Zbl 1131.65046
Hofmann, B.; Kaltenbacher, B.; Pöschl, C.; Scherzer, O.
150
2007
Analysis of profile functions for general linear regularization methods. Zbl 1137.47063
Hofmann, Bernd; Mathé, Peter
40
2007
Range inclusions and approximate source conditions with general benchmark functions. Zbl 1136.47008
Düvelmeyer, Dana; Hofmann, Bernd; Yamamoto, Masahiro
10
2007
Regularization by projection: approximation theoretic aspects and distance functions. Zbl 1134.65039
Hofmann, B.; Mathé, P.; Pereverzev, S. V.
10
2007
On the analysis of distance functions for linear ill-posed problems with an application to the integration operator in \(L^2\). Zbl 1123.47014
Hofmann, B.; Schieck, M.; von Wolfersdorf, L.
5
2007
Approximate source conditions in Tikhonov–Phillips regularization and consequences for inverse problems with multiplication operators. Zbl 1094.47015
Hofmann, Bernd
28
2006
On decoupling of volatility smile and term structure in inverse option pricing. Zbl 1112.91032
Egger, Herbert; Hein, Torsten; Hofmann, Bernd
24
2006
Convergence rates for Tikhonov regularization from different kinds of smoothness conditions. Zbl 1110.65041
Böttcher, Albrecht; Hofmann, Bernd; Tautenhahn, Ulrich; Yamamoto, Masahiro
23
2006
A multi-parameter regularization approach for estimating parameters in jump diffusion processes. Zbl 1105.62103
Düvelmeyer, D.; Hofmann, B.
7
2006
On the determination of a density function by its autoconvolution coefficient. Zbl 1099.47049
Hofmann, Bernd; von Wolfersdorf, Lothar
5
2006
Approximate source conditions in Tikhonov regularization – new analytical results and some numerical studies. Zbl 1110.65043
Hofmann, B.; Düvelmeyer, D.; Krumbiegel, K.
3
2006
On maximum entropy regularization for a specific inverse problem of option pricing. Zbl 1086.91029
Hofmann, B.; Krämer, R.
12
2005
Convergence rates for Tikhonov regularization based on range inclusions. Zbl 1077.65056
Hofmann, Bernd; Yamamoto, Masahiro
12
2005
Some results and a conjecture on the degree of ill-posedness for integration operators with weights. Zbl 1080.47015
Hofmann, Bernd; von Wolfersdorf, Lothar
8
2005
Analytical and numerical studies on the influence of multiplication operators for the ill-posedness of inverse problems. Zbl 1083.65054
Freitag, M.; Hofmann, B.
7
2005
On the nature of ill-posedness of an inverse problem arising in option pricing. Zbl 1086.91028
Hein, Torsten; Hofmann, Bernd
28
2003
Well-posed and ill-posed situations in option pricing problems when the volatility is purely time-dependent. Zbl 1354.91149
Hofmann, Bernd; Hein, Torsten
2
2003
Ill-posedness and local ill-posedness concepts in Hilbert spaces. Zbl 0981.65072
Hofmann, Bernd
4
2000
Mathematics of inverse problems. (Mathematik inverser Probleme.) Zbl 0942.45004
Hofmann, Bernd
6
1999
On the autoconvolution equation and total variation constraints. Zbl 0923.65098
Fleischer, G.; Gorenflo, R.; Hofmann, B.
4
1999
Stability rates for linear ill-posed problems with compact and non-compact operators. Zbl 0941.65055
Hofmann, B.; Fleischer, G.
2
1999
A denseness theorem with an application to a two-dimensional inverse potential refraction problem. Zbl 0937.35183
Hofmann, Bernd
1
1999
Local ill-posedness and source conditions of operator equations in Hilbert spaces. Zbl 0915.65052
Hofmann, Bernd; Scherzer, Otmar
13
1998
Approximation of the inverse electrical impedance tomography problem by an inverse transmission problem. Zbl 0992.78020
Hofmann, B.
2
1998
On ill-posedness measures and space change in Sobolev scales. Zbl 0896.65043
Hofmann, B.; Tautenhahn, U.
4
1997
The local degree of ill-posedness and the autoconvolution equation. Zbl 0894.47048
Fleischer, Gunter; Hofmann, Bernd
1
1997
On inversion rates for the autoconvolution equation. Zbl 0862.45007
Fleischer, Gunter; Hofmann, Bernd
12
1996
Decomposition cases of nonlinear ill-posed problems. Zbl 0886.47035
Hofmann, B.; Schröter, T.
1
1996
Ill-posedness and regularization of inverse problem – a review of mathematical methods. Zbl 0923.35205
Hofmann, Bernd
1
1995
Factors influencing the ill-posedness of nonlinear problems. Zbl 0809.35157
Hofmann, Bernd; Scherzer, Otmar
35
1994
On autoconvolution and regularization. Zbl 0804.45003
Gorenflo, Rudolf; Hofmann, Bernd
34
1994
On the degree of ill-posedness for nonlinear problems. Zbl 0818.35137
Hofmann, B.
13
1994
A study of regularization by monotonicity. Zbl 0774.65099
Gellrich, C.; Hofmann, B.
5
1993
A decreasing rearrangement approach for a class of ill-posed nonlinear integral equations. Zbl 0799.65149
Engl, Heinz W.; Hofmann, Bernd; Zeisel, Helmut
2
1993
Regularization of nonlinear problems and the degree of ill-posedness. Zbl 0812.47065
Hofmann, Bernd
1
1993
On a class of ill-posed nonlinear integral equations arising in the interpretation of indirect measurements. Zbl 0742.65100
Hofmann, Bernd
3
1991
Uniqueness of monotone solutions to a non-linear Fredholm integral equation. Zbl 0733.45008
Hofmann, B.; Schachtzabel, H.
3
1991
Regularization of a Volterra integral equation by linear inequalities. Zbl 0697.65095
Hofmann, B.; Hausding, R.; Wolke, R.
2
1990
On a class of ill-posed integral equations with curious properties. Zbl 0691.45009
Hofmann, Bernd
1
1989
On the analysis of a particular Volterra-Stieltjes convolution integral equation. Zbl 0653.45003
Hofmann, B.
1
1988
A predictor-corrector technique for constrained least-squares regularization. Zbl 0616.65062
Friedrich, Volkmar; Hofmann, Bernd
2
1987
Regularization for applied inverse and ill-posed problems. A numerical approach. Zbl 0606.65038
Hofmann, Bernd
56
1986
Optimization aspects of the generalized discrepancy principle in regularization. Zbl 0592.65021
Hofmann, B.
5
1986
Zur Regularisierung nichtlinearer inverser Probleme. Zbl 0512.65048
Hofmann, Bernd
1
1982
Die Methode der Quasiinversion als Regularisierungsverfahren im Hilbertraum. Zbl 0457.65040
Hofmann, Bernd
1
1981
...and 2 more Documents
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Cited by 775 Authors

65 Hofmann, Bernd
28 Mathé, Peter
22 Han, Bo
21 Kaltenbacher, Barbara
21 Scherzer, Otmar
16 Jin, Qinian
16 Pereverzev, Sergei V.
14 Lu, Shuai
13 Hohage, Thorsten
13 Wang, Wei
12 Burger, Martin
12 Tautenhahn, Ulrich
11 Gerth, Daniel
11 Kindermann, Stefan
11 Zhang, Ye
10 von Wolfersdorf, Lothar
9 Jin, Bangti
8 Chen, Dehan
8 Fu, Zhenwu
8 Giri, Ankik Kumar
8 Mittal, Gaurav
8 Ramlau, Ronny
7 Chen, Yong
7 Flemming, Jens
7 George, Santhosh
7 Gu, Ruixue
7 Haltmeier, Markus
7 Holler, Martin
7 Jia, Zhongxiao
7 Schuster, Thomas
7 Zou, Jun
6 Bredies, Kristian
6 Clason, Christian
6 Mahale, Pallavi
6 Margotti, Fábio
6 Nair, M. Thamban
6 Plato, Robert
6 Tkachenko, Pavlo
6 Tong, Shanshan
6 Wald, Anne
6 Zheng, Guanghui
6 Zhong, Min
5 Albani, Vinicius V. L.
5 Bockmann, Christine
5 Estatico, Claudio
5 Hein, Torsten
5 Khan, Akhtar Ali
5 Lu, Xiliang
5 Nguyen, Tram Thi Ngoc
5 Pereverzyev, Sergiy jun.
5 Xia, Yuxin
5 Xiong, Xiangtuan
5 Yousept, Irwin
5 Zubelli, Jorge P.
4 Boţ, Radu Ioan
4 De Cezaro, Adriano
4 Dixit, Sharad Kumar
4 Dong, Guozhi
4 Engl, Heinz W.
4 Frikel, Jürgen
4 Gong, Rongfang
4 Grasmair, Markus
4 Hämarik, Uno
4 Hubmer, Simon
4 Lechleiter, Armin
4 Lorenz, Dirk Alfred
4 Maass, Peter
4 Miller, Philip H.
4 Neubauer, Andreas
4 Ouakrim, Youssef
4 Quyen, Tran Nhan Tam
4 Resmerita, Elena
4 Sama, Miguel
4 Schieck, M.
4 Smirnova, Alexandra B.
4 Werner, Frank
4 Yamamoto, Masahiro
3 Argyros, Ioannis Konstantinos
3 Bakushinskĭ, Anatoliĭ Borisovich B.
3 Bubba, Tatiana A.
3 Cheng, Jin
3 de Hoop, Maarten V.
3 Ding, Liang
3 Egger, Herbert
3 Elbau, Peter
3 Ellabib, Abdellatif
3 Ernst, Oliver G.
3 Fury, Matthew A.
3 Iglesias, José Antonio
3 Ito, Kazufumi
3 Jadamba, Baasansuren
3 Janno, Jaan
3 Jiang, Daijun
3 Kabanikhin, Sergeĭ Igorevich
3 Kazimierski, Kamil S.
3 Kirisits, Clemens
3 Klassen, Andrej
3 Klibanov, Michael V.
3 Kluth, Tobias
3 Kunisch, Karl
...and 675 more Authors
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Cited in 128 Serials

112 Inverse Problems
52 Journal of Inverse and Ill-Posed Problems
27 Applicable Analysis
25 Journal of Computational and Applied Mathematics
23 Numerical Functional Analysis and Optimization
20 Inverse Problems and Imaging
19 Inverse Problems in Science and Engineering
16 Numerische Mathematik
12 SIAM Journal on Numerical Analysis
12 ETNA. Electronic Transactions on Numerical Analysis
11 Applied Numerical Mathematics
11 Journal of Integral Equations and Applications
10 Journal of Mathematical Analysis and Applications
8 Mathematics of Computation
8 Optimization
8 Journal of Complexity
8 Numerical Algorithms
8 SIAM Journal on Imaging Sciences
7 Applied Mathematics and Computation
7 Zeitschrift für Analysis und ihre Anwendungen
6 Journal of Computational Physics
5 Applied Mathematics Letters
5 Journal of Mathematical Imaging and Vision
5 Computational Optimization and Applications
5 Applied and Computational Harmonic Analysis
5 Foundations of Computational Mathematics
5 Analysis and Applications (Singapore)
5 Electronic Journal of Statistics
5 GEM - International Journal on Geomathematics
5 AIMS Mathematics
4 Computers & Mathematics with Applications
4 Mathematical Methods in the Applied Sciences
4 BIT
4 Computing
4 Journal of Optimization Theory and Applications
4 Mathematics and Computers in Simulation
4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
4 Nonlinear Analysis. Real World Applications
4 International Journal of Computational Methods
3 Journal of Approximation Theory
3 SIAM Journal on Optimization
3 SIAM Journal on Scientific Computing
3 Mathematical Problems in Engineering
3 Fractional Calculus & Applied Analysis
3 Computational Methods in Applied Mathematics
3 Science China. Mathematics
3 SIAM/ASA Journal on Uncertainty Quantification
2 The Annals of Statistics
2 Applied Mathematics and Optimization
2 Calcolo
2 Journal of Econometrics
2 Journal of Scientific Computing
2 Computational Mathematics and Mathematical Physics
2 Communications in Statistics. Theory and Methods
2 International Journal of Computer Mathematics
2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
2 Computational and Applied Mathematics
2 Journal of Convex Analysis
2 Integral Transforms and Special Functions
2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
2 Russian Physics Journal
2 Mathematical Modelling and Analysis
2 Journal of Applied Mathematics and Computing
2 Milan Journal of Mathematics
2 Acta Numerica
2 Nonlinear Analysis. Theory, Methods & Applications
2 Journal of Nonlinear and Variational Analysis
1 Communications on Pure and Applied Mathematics
1 Journal of Mathematical Biology
1 Annals of the Institute of Statistical Mathematics
1 Journal of Differential Equations
1 Journal of Soviet Mathematics
1 Rendiconti del Circolo Matemàtico di Palermo. Serie II
1 Revista de la Unión Matemática Argentina
1 Chinese Annals of Mathematics. Series B
1 Journal of Computational Mathematics
1 Statistics
1 Computational Mechanics
1 Journal of Economic Dynamics & Control
1 Mathematical and Computer Modelling
1 Neural Networks
1 Machine Learning
1 Japan Journal of Industrial and Applied Mathematics
1 Linear Algebra and its Applications
1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
1 SIAM Journal on Applied Mathematics
1 SIAM Journal on Mathematical Analysis
1 SIAM Review
1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
1 Journal of Partial Differential Equations
1 Mathematical Methods of Statistics
1 Journal of Mathematical Sciences (New York)
1 Numerical Linear Algebra with Applications
1 International Journal of Computer Vision
1 Advances in Computational Mathematics
1 Applied Mathematical Finance
1 Engineering Analysis with Boundary Elements
1 Journal of Geodesy
1 Discrete and Continuous Dynamical Systems
1 Finance and Stochastics
...and 28 more Serials
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Cited in 39 Fields

484 Numerical analysis (65-XX)
251 Operator theory (47-XX)
156 Partial differential equations (35-XX)
73 Calculus of variations and optimal control; optimization (49-XX)
61 Integral equations (45-XX)
50 Statistics (62-XX)
35 Biology and other natural sciences (92-XX)
34 Information and communication theory, circuits (94-XX)
33 Computer science (68-XX)
32 Operations research, mathematical programming (90-XX)
32 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
23 Functional analysis (46-XX)
23 Optics, electromagnetic theory (78-XX)
21 Probability theory and stochastic processes (60-XX)
19 Geophysics (86-XX)
15 Mechanics of deformable solids (74-XX)
12 Real functions (26-XX)
9 Approximations and expansions (41-XX)
8 Fluid mechanics (76-XX)
7 Systems theory; control (93-XX)
6 Ordinary differential equations (34-XX)
6 Integral transforms, operational calculus (44-XX)
4 Linear and multilinear algebra; matrix theory (15-XX)
4 Functions of a complex variable (30-XX)
4 Harmonic analysis on Euclidean spaces (42-XX)
4 Classical thermodynamics, heat transfer (80-XX)
3 Statistical mechanics, structure of matter (82-XX)
2 Special functions (33-XX)
2 Convex and discrete geometry (52-XX)
2 Differential geometry (53-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Combinatorics (05-XX)
1 Potential theory (31-XX)
1 Abstract harmonic analysis (43-XX)
1 General topology (54-XX)
1 Mechanics of particles and systems (70-XX)
1 Astronomy and astrophysics (85-XX)
1 Mathematics education (97-XX)

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