Edit Profile (opens in new tab) Hofmann, Bernd Co-Author Distance Author ID: hofmann.bernd Published as: Hofmann, Bernd; Hofmann, B. External Links: MGP Documents Indexed: 149 Publications since 1979, including 3 Books and 9 Additional arXiv Preprints 2 Contributions as Editor Reviewing Activity: 154 Reviews Co-Authors: 92 Co-Authors with 115 Joint Publications 3,030 Co-Co-Authors all top 5 Co-Authors 32 single-authored 18 Mathé, Peter 8 Plato, Robert 7 Flemming, Jens 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 Werner, Frank 3 Yagola, Anatoliĭ Grigor’evich 2 Egger, Herbert 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 Engl, Heinz W. 1 Gellrich, Carsten 1 Gong, Rongfang 1 Hämarik, Uno 1 Hausding, Reiner 1 Hegland, Markus 1 Hinneberg, Hans-Jürgen 1 Hinze, Michael 1 Kazimierski, Kamil S. 1 Klinkhammer, Chantal 1 Koke, Sebastian 1 Koutschan, Christoph 1 Krumbiegel, Klaus 1 Kuchuk, Fikri J. 1 Leitão, Antonio 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 Quyen, Tran Nhan Tam 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 1 Zubelli, Jorge P. all top 5 Serials 29 Inverse Problems 15 Journal of Inverse and Ill-Posed Problems 8 Applicable Analysis 6 Zeitschrift für Analysis und ihre Anwendungen 5 Numerical Functional Analysis and Optimization 5 ETNA. Electronic Transactions on Numerical Analysis 4 Wissenschaftliche Zeitschrift der Technischen Hochschule Karl-Marx-Stadt 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 Trends in Mathematics 1 AIMS Mathematics 1 Sampling Theory, Signal Processing, and Data Analysis all top 5 Fields 121 Numerical analysis (65-XX) 86 Operator theory (47-XX) 31 Integral equations (45-XX) 24 Partial differential equations (35-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Integral transforms, operational calculus (44-XX) 7 Statistics (62-XX) 5 Operations research, mathematical programming (90-XX) 4 Optics, electromagnetic theory (78-XX) 3 History and biography (01-XX) 3 Ordinary differential equations (34-XX) 3 Probability theory and stochastic processes (60-XX) 3 Biology and other natural sciences (92-XX) 2 General and overarching topics; collections (00-XX) 2 Real functions (26-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Mechanics of deformable solids (74-XX) 1 Potential theory (31-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Functional analysis (46-XX) 1 Computer science (68-XX) 1 Fluid mechanics (76-XX) 1 Geophysics (86-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 107 Publications have been cited 1,421 times in 674 Documents Cited by ▼ Year ▼ Regularization methods in Banach spaces. Zbl 1259.65087 Schuster, Thomas; Kaltenbacher, Barbara; Hofmann, Bernd; Kazimierski, Kamil S. 211 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 57 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 31 2010 Parameter choice in Banach space regularization under variational inequalities. Zbl 1253.47041 Hofmann, Bernd; Mathé, Peter 30 2012 On the nature of ill-posedness of an inverse problem arising in option pricing. Zbl 1086.91028 Hein, Torsten; Hofmann, Bernd 28 2003 Approximate source conditions in Tikhonov–Phillips regularization and consequences for inverse problems with multiplication operators. Zbl 1094.47015 Hofmann, Bernd 28 2006 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 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 in \(\ell^1\)-regularization if the sparsity assumption fails. Zbl 1262.49010 Burger, Martin; Flemming, Jens; Hofmann, Bernd 24 2013 Convergence rates for Tikhonov regularization from different kinds of smoothness conditions. Zbl 1110.65041 Böttcher, Albrecht; Hofmann, Bernd; Tautenhahn, Ulrich; Yamamoto, Masahiro 23 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 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 20 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 Tikhonov regularization in Hilbert scales under conditional stability assumptions. Zbl 1415.65130 Egger, H.; Hofmann, B. 18 2018 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 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 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 Convergence analysis of (statistical) inverse problems under conditional stability estimates. Zbl 1485.65059 Werner, Frank; Hofmann, Bernd 13 2020 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 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 inversion rates for the autoconvolution equation. Zbl 0862.45007 Fleischer, Gunter; Hofmann, Bernd 12 1996 On ill-posedness concepts, stable solvability and saturation. Zbl 1492.47019 Hofmann, Bernd; Plato, Robert 11 2018 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 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 The index function and Tikhonov regularization for ill-posed problems. Zbl 1293.65086 Cheng, Jin; Hofmann, Bernd; Lu, Shuai 8 2014 On complex-valued deautoconvolution of compactly supported functions with sparse Fourier representation. Zbl 1431.47005 Bürger, Steven; Flemming, Jens; Hofmann, Bernd 8 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 Regularization and convergence for ill-posed backward evolution equations in Banach spaces. Zbl 06901111 Chen, De-Han; Hofmann, Bernd; Zou, Jun 8 2018 Regularization in Hilbert space under unbounded operators and general source conditions. Zbl 1178.47006 Hofmann, Bernd; Mathé, Peter; von Weizsäcker, Heinrich 7 2009 Convergence rates in constrained Tikhonov regularization: equivalence of projected source conditions and variational inequalities. Zbl 1233.47053 Flemming, Jens; Hofmann, Bernd 7 2011 A multi-parameter regularization approach for estimating parameters in jump diffusion processes. Zbl 1105.62103 Düvelmeyer, D.; Hofmann, B. 7 2006 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 Mathematics of inverse problems. (Mathematik inverser Probleme.) Zbl 0942.45004 Hofmann, Bernd 7 1999 Direct and inverse results in variable Hilbert scales. Zbl 1169.41003 Mathé, Peter; Hofmann, Bernd 7 2008 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 the degree of ill-posedness for linear problems with noncompact operators. Zbl 1228.47017 Hofmann, Bernd; Kindermann, Stefan 6 2010 Optimal rates for Lavrentiev regularization with adjoint source conditions. Zbl 1380.65096 Plato, Robert; Mathé, Peter; Hofmann, Bernd 6 2018 A regularization approach for an inverse source problem in elliptic systems from single Cauchy data. Zbl 1412.65040 Hinze, Michael; Hofmann, Bernd; Quyen, Tran Nhan Tam 6 2019 Convergence results and low-order rates for nonlinear Tikhonov regularization with oversmoothing penalty term. Zbl 07192776 Hofmann, Bernd; Plato, Robert 6 2020 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 Optimization aspects of the generalized discrepancy principle in regularization. Zbl 0592.65021 Hofmann, B. 5 1986 A study of regularization by monotonicity. Zbl 0774.65099 Gellrich, C.; Hofmann, B. 5 1993 On \(\ell^1\)-regularization in light of Nashed’s ill-posedness concept. Zbl 1319.47006 Flemming, Jens; Hofmann, Bernd; Veselić, Ivan 5 2015 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 5 2019 A specific inverse problem for the Volterra convolution equation. Zbl 1148.45014 von Wolfersdorf, Lothar; Hofmann, Bernd 4 2008 Ill-posedness and local ill-posedness concepts in Hilbert spaces. Zbl 0981.65072 Hofmann, Bernd 4 2000 On the autoconvolution equation and total variation constraints. Zbl 0923.65098 Fleischer, G.; Gorenflo, R.; Hofmann, B. 4 1999 On ill-posedness measures and space change in Sobolev scales. Zbl 0896.65043 Hofmann, B.; Tautenhahn, U. 4 1997 Conditional stability versus ill-posedness for operator equations with monotone operators in Hilbert space. Zbl 1368.47044 Boţ, Radu Ioan; Hofmann, Bernd 4 2016 Oversmoothing regularization with \(\ell^1\)-penalty term. Zbl 1484.47021 Gerth, Daniel; Hofmann, Bernd 4 2019 A priori parameter choice in Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems. Zbl 1437.65048 Hofmann, Bernd; Mathé, Peter 4 2020 Regularizability of ill-posed problems and the modulus of continuity. Zbl 1288.47015 Boţ, Radu Ioan; Hofmann, Bernd; Mathé, Peter 4 2013 Oversmoothing Tikhonov regularization in Banach spaces. Zbl 1483.65086 Chen, De-Han; Hofmann, Bernd; Yousept, Irwin 4 2021 Regularization methods for ill-posed problems. Zbl 1259.65086 Cheng, Jin; Hofmann, Bernd 4 2011 Penalty-based smoothness conditions in convex variational regularization. Zbl 1483.65087 Hofmann, Bernd; Kindermann, Stefan; Mathé, Peter 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 Uniqueness of monotone solutions to a non-linear Fredholm integral equation. Zbl 0733.45008 Hofmann, B.; Schachtzabel, H. 3 1991 On a class of ill-posed nonlinear integral equations arising in the interpretation of indirect measurements. Zbl 0742.65100 Hofmann, Bernd 3 1991 Case studies and a pitfall for nonlinear variational regularization under conditional stability. Zbl 1443.65080 Gerth, Daniel; Hofmann, Bernd; Hofmann, Christopher 3 2020 Approximation of the inverse electrical impedance tomography problem by an inverse transmission problem. Zbl 0992.78020 Hofmann, B. 2 1998 Errors of regularisation under range inclusions using variable Hilbert scales. Zbl 1252.47009 Hegland, Markus; Hofmann, Bernd 2 2011 Stability rates for linear ill-posed problems with compact and non-compact operators. Zbl 0941.65055 Hofmann, B.; Fleischer, G. 2 1999 A predictor-corrector technique for constrained least-squares regularization. Zbl 0616.65062 Friedrich, Volkmar; Hofmann, Bernd 2 1987 Regularization of a Volterra integral equation by linear inequalities. Zbl 0697.65095 Hofmann, B.; Hausding, R.; Wolke, R. 2 1990 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 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 A new result in the singular value asymptotics of integration operators with weights. Zbl 1167.45303 Hofmann, Bernd; Von Wolfersdorf, Lothar 2 2009 Regularization methods for ill-posed problems. 2nd edition. Zbl 1331.65081 Cheng, Jin; Hofmann, Bernd 2 2015 On the singular value decomposition of \(n\)-fold integration operators. Zbl 1512.47020 Ramlau, Ronny; Koutschan, Christoph; Hofmann, Bernd 2 2020 Two new non-negativity preserving iterative regularization methods for ill-posed inverse problems. Zbl 1520.47029 Zhang, Ye; Hofmann, Bernd 2 2021 On the analysis of a particular Volterra-Stieltjes convolution integral equation. Zbl 0653.45003 Hofmann, B. 1 1988 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 On a class of ill-posed integral equations with curious properties. Zbl 0691.45009 Hofmann, Bernd 1 1989 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 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 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 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 Regularization of linear ill-posed problems involving multiplication operators. Zbl 07495666 Mathé, P.; Nair, M. T.; Hofmann, B. 1 2022 Oversmoothing Tikhonov regularization in Banach spaces. Zbl 1483.65086 Chen, De-Han; Hofmann, Bernd; Yousept, Irwin 4 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 13 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 6 2020 A priori parameter choice in Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems. Zbl 1437.65048 Hofmann, Bernd; Mathé, Peter 4 2020 Case studies and a pitfall for nonlinear variational regularization under conditional stability. Zbl 1443.65080 Gerth, Daniel; Hofmann, Bernd; Hofmann, Christopher 3 2020 On the singular value decomposition of \(n\)-fold integration operators. Zbl 1512.47020 Ramlau, Ronny; Koutschan, Christoph; Hofmann, Bernd 2 2020 On fractional asymptotical regularization of linear ill-posed problems in Hilbert spaces. Zbl 1478.65059 Zhang, Ye; Hofmann, Bernd 11 2019 A regularization approach for an inverse source problem in elliptic systems from single Cauchy data. Zbl 1412.65040 Hinze, Michael; Hofmann, Bernd; Quyen, Tran Nhan Tam 6 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 5 2019 Oversmoothing regularization with \(\ell^1\)-penalty term. Zbl 1484.47021 Gerth, Daniel; Hofmann, Bernd 4 2019 Penalty-based smoothness conditions in convex variational regularization. Zbl 1483.65087 Hofmann, Bernd; Kindermann, Stefan; Mathé, Peter 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 20 2018 Tikhonov regularization in Hilbert scales under conditional stability assumptions. Zbl 1415.65130 Egger, H.; Hofmann, B. 18 2018 On ill-posedness concepts, stable solvability and saturation. Zbl 1492.47019 Hofmann, Bernd; Plato, Robert 11 2018 Regularization and convergence for ill-posed backward evolution equations in Banach spaces. Zbl 06901111 Chen, De-Han; Hofmann, Bernd; Zou, Jun 8 2018 Optimal rates for Lavrentiev regularization with adjoint source conditions. Zbl 1380.65096 Plato, Robert; Mathé, Peter; Hofmann, Bernd 6 2018 New trends in parameter identification for mathematical models. Proceedings of the conference, Rio de Janeiro, Brazil, October 30 – November 3, 2017. Zbl 1392.65007 1 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 On complex-valued deautoconvolution of compactly supported functions with sparse Fourier representation. Zbl 1431.47005 Bürger, Steven; Flemming, Jens; Hofmann, Bernd 8 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 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. 211 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 4 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 31 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 6 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 7 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 Uniqueness of monotone solutions to a non-linear Fredholm integral equation. Zbl 0733.45008 Hofmann, B.; Schachtzabel, H. 3 1991 On a class of ill-posed nonlinear integral equations arising in the interpretation of indirect measurements. Zbl 0742.65100 Hofmann, Bernd 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 ...and 7 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 793 Authors 68 Hofmann, Bernd 28 Mathé, Peter 22 Han, Bo 21 Kaltenbacher, Barbara 21 Scherzer, Otmar 16 Jin, Qinian 16 Pereverzev, Sergei V. 14 Lu, Shuai 14 Wang, Wei 13 Hohage, Thorsten 12 Burger, Martin 12 Tautenhahn, Ulrich 11 Gerth, Daniel 11 Kindermann, Stefan 11 Werner, Frank 11 Zhang, Ye 10 Giri, Ankik Kumar 10 Jin, Bangti 10 Mittal, Gaurav 10 von Wolfersdorf, Lothar 9 George, Santhosh 9 Ramlau, Ronny 8 Chen, Dehan 8 Fu, Zhenwu 7 Chen, Yong 7 Flemming, Jens 7 Gu, Ruixue 7 Haltmeier, Markus 7 Holler, Martin 7 Jia, Zhongxiao 7 Nair, M. Thamban 7 Schuster, Thomas 7 Tong, Shanshan 7 Zou, Jun 6 Bredies, Kristian 6 Clason, Christian 6 Khan, Akhtar Ali 6 Mahale, Pallavi 6 Margotti, Fábio 6 Plato, Robert 6 Quyen, Tran Nhan Tam 6 Tkachenko, Pavlo 6 Wald, Anne 6 Zheng, Guanghui 6 Zhong, Min 5 Albani, Vinicius V. L. 5 Bockmann, Christine 5 Estatico, Claudio 5 Hein, Torsten 5 Hubmer, Simon 5 Lu, Xiliang 5 Nguyen, Tram Thi Ngoc 5 Pereverzyev, Sergiy jun. 5 Sama, Miguel 5 Xia, Yuxin 5 Xiong, Xiangtuan 5 Yousept, Irwin 5 Zubelli, Jorge P. 4 Boţ, Radu Ioan 4 De Cezaro, Adriano 4 Ding, Liang 4 Dixit, Sharad Kumar 4 Dong, Guozhi 4 Engl, Heinz W. 4 Frikel, Jürgen 4 Fury, Matthew A. 4 Gong, Rongfang 4 Grasmair, Markus 4 Hämarik, Uno 4 Jidesh, P. 4 Lechleiter, Armin 4 Lorenz, Dirk Alfred 4 Maass, Peter 4 Miller, Philip H. 4 Neubauer, Andreas 4 Ouakrim, Youssef 4 Resmerita, Elena 4 Schieck, M. 4 Smirnova, Alexandra B. 4 Yamamoto, Masahiro 4 Zhang, Hongwu 3 Argyros, Ioannis Konstantinos 3 Bakushinskĭ, Anatoliĭ Borisovich B. 3 Bubba, Tatiana A. 3 Cao, Kai 3 Cheng, Jin 3 de Hoop, Maarten V. 3 Đinh Nho Hào 3 Egger, Herbert 3 Elbau, Peter 3 Ellabib, Abdellatif 3 Ernst, Oliver G. 3 Hahn, Bernadette Nadine 3 Iglesias, José Antonio 3 Ito, Kazufumi 3 Jadamba, Baasansuren 3 Janno, Jaan 3 Jiang, Daijun 3 Kabanikhin, Sergeĭ Igorevich 3 Kazimierski, Kamil S. ...and 693 more Authors all top 5 Cited in 134 Serials 116 Inverse Problems 56 Journal of Inverse and Ill-Posed Problems 29 Applicable Analysis 26 Journal of Computational and Applied Mathematics 23 Numerical Functional Analysis and Optimization 22 Inverse Problems and Imaging 20 Inverse Problems in Science and Engineering 17 Numerische Mathematik 13 SIAM Journal on Numerical Analysis 12 Applied Numerical Mathematics 12 ETNA. Electronic Transactions on Numerical Analysis 11 Journal of Integral Equations and Applications 10 Journal of Mathematical Analysis and Applications 9 Applied Mathematics and Computation 8 Mathematics of Computation 8 Optimization 8 Journal of Complexity 8 Numerical Algorithms 8 SIAM Journal on Imaging Sciences 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 Applied Mathematics and Optimization 3 Journal of Approximation Theory 3 Computational Mathematics and Mathematical Physics 3 SIAM Journal on Optimization 3 SIAM Journal on Scientific Computing 3 Computational and Applied Mathematics 3 Journal of Convex Analysis 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 Calcolo 2 Journal of Econometrics 2 Journal of Scientific Computing 2 Communications in Statistics. Theory and Methods 2 International Journal of Computer Mathematics 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 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 GAMM-Mitteilungen 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 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Annals of the Institute of Statistical Mathematics 1 Archiv der Mathematik 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 Numerical Methods for Partial Differential Equations 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 The Journal of Analysis 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 ...and 34 more Serials all top 5 Cited in 39 Fields 510 Numerical analysis (65-XX) 262 Operator theory (47-XX) 170 Partial differential equations (35-XX) 80 Calculus of variations and optimal control; optimization (49-XX) 61 Integral equations (45-XX) 49 Statistics (62-XX) 37 Biology and other natural sciences (92-XX) 34 Operations research, mathematical programming (90-XX) 34 Information and communication theory, circuits (94-XX) 33 Computer science (68-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) 14 Real functions (26-XX) 9 Approximations and expansions (41-XX) 8 Fluid mechanics (76-XX) 7 Ordinary differential equations (34-XX) 7 Systems theory; control (93-XX) 6 Integral transforms, operational calculus (44-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Functions of a complex variable (30-XX) 4 Special functions (33-XX) 3 Statistical mechanics, structure of matter (82-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) Citations by Year