## Hanke-Bourgeois, Martin

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 Author ID: hanke-bourgeois.martin Published as: Hanke, Martin; Hanke-Bourgeois, Martin; Hanke, M. more...less Homepage: http://www.mathematik.uni-mainz.de/Members/hanke External Links: MGP
 Documents Indexed: 104 Publications since 1988, including 7 Books 3 Contributions as Editor Co-Authors: 42 Co-Authors with 63 Joint Publications 1,141 Co-Co-Authors
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### Co-Authors

 36 single-authored 8 Griesmaier, Roland 7 Hyvönen, Nuutti 6 Kirsch, Andreas 5 Hollborn, Stefanie 5 Nagy, James Gerard 4 Brühl, Martin 4 Niethammer, Wilhelm 4 Scherzer, Otmar 3 Engl, Heinz W. 3 Groetsch, Charles W. 3 Harrach, Bastian 3 Hochbruck, Marlis 3 Neubauer, Andreas 3 Rundell, William 2 Donatelli, Marco 2 Frommer, Fabio 2 Hansen, Per Christian 2 Neumann, Michael 2 Raasch, Thorsten 2 Schneider, Christoph 2 Vogel, Curtis R. 1 Ammari, Habib M. 1 Ballmann, Josef 1 Binder, Andreas 1 Cakoni, Fioralba 1 Chaudhry, Qasim Ali 1 Christiansen, Martin 1 Delbary, Fabrice 1 Drey, Klaus-Dieter 1 Egger, Herbert 1 Eich, Edda 1 Fischer, Bernd 1 Frankenberger, Harald 1 Gohberg, Israel 1 Harhanen, Lauri 1 Ivanizki, Dmitry 1 Koltracht, Israel 1 Lassas, Matti J. 1 Lehn, Manfred 1 Loubenets, A. 1 Muniz, Wagner Barbosa 1 Pidcock, Michael K. 1 Plemmons, Robert James 1 Porz, Nikolas 1 Pötzelberger, Klaus 1 Raus, Toomas 1 Rösler, Elisabeth 1 Schappel, Birgit 1 Schneider, Claus B. 1 Schöberl, Joachim 1 Schweickert, Eva 1 Sylvester, John Herbert 1 Vogelius, Michael S. 1 Warth, L. 1 Zaglmayr, Sabine
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### Serials

 11 Inverse Problems 7 Numerische Mathematik 6 Linear Algebra and its Applications 4 BIT 4 SIAM Journal on Numerical Analysis 4 Zeitschrift für Analysis und ihre Anwendungen 4 Numerical Algorithms 4 SIAM Journal on Scientific Computing 3 Letters in Mathematical Physics 3 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 3 Numerical Functional Analysis and Optimization 3 SIAM Journal on Applied Mathematics 3 Oberwolfach Reports 3 SIAM Journal on Imaging Sciences 2 Journal of Computational and Applied Mathematics 2 SIAM Journal on Mathematical Analysis 2 ETNA. Electronic Transactions on Numerical Analysis 2 Inverse Problems and Imaging 1 American Mathematical Monthly 1 Applicable Analysis 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Mathematics of Computation 1 Journal of Approximation Theory 1 Journal of Optimization Theory and Applications 1 Proceedings of the American Mathematical Society 1 Applied Numerical Mathematics 1 Journal of Integral Equations and Applications 1 Surveys on Mathematics for Industry 1 Applications of Mathematics 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Journal of Inverse and Ill-Posed Problems 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 International Journal of Theoretical and Applied Finance 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Quantitative Finance 1 Inverse Problems in Science and Engineering 1 Mathematics and its Applications (Dordrecht) 1 Other Titles in Applied Mathematics
all top 5

### Fields

 78 Numerical analysis (65-XX) 38 Partial differential equations (35-XX) 25 Operator theory (47-XX) 21 Optics, electromagnetic theory (78-XX) 9 Integral equations (45-XX) 7 Statistical mechanics, structure of matter (82-XX) 7 Information and communication theory, circuits (94-XX) 6 Ordinary differential equations (34-XX) 6 Biology and other natural sciences (92-XX) 5 Computer science (68-XX) 4 General and overarching topics; collections (00-XX) 3 Approximations and expansions (41-XX) 3 Integral transforms, operational calculus (44-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Potential theory (31-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistics (62-XX) 2 Fluid mechanics (76-XX) 2 Geophysics (86-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX)

### Citations contained in zbMATH Open

88 Publications have been cited 2,820 times in 2,053 Documents Cited by Year
Regularization of inverse problems. Zbl 0859.65054
Engl, Heinz W.; Hanke, Martin; Neubauer, Andreas
1996
A convergence analysis of the Landweber iteration for nonlinear ill-posed problems. Zbl 0840.65049
Hanke, Martin; Neubauer, Andreas; Scherzer, Otmar
1995
Regularization methods for large-scale problems. Zbl 0805.65058
Hanke, Martin; Hansen, Per Christian
1993
A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems. Zbl 0873.65057
Hanke, Martin
1997
Conjugate gradient type methods for ill-posed problems. Zbl 0830.65043
Hanke, Martin
1995
Inverse problems light: Numerical differentiation. Zbl 1002.65029
Hanke, Martin; Scherzer, Otmar
2001
Tikhonov regularization of nonlinear differential-algebraic equations. Zbl 0711.34018
Engl, H. W.; Hanke, M.; Neubauer, A.
1990
Numerical implementation of two noniterative methods for locating inclusions by impedance tomography. Zbl 0955.35076
Brühl, Martin; Hanke, Martin
2000
A direct impedance tomography algorithm for locating small inhomogeneities. Zbl 1016.65079
Brühl, Martin; Hanke, Martin; Vogelius, Michael S.
2003
Preconditioned iterative regularization for ill-posed problems. Zbl 0794.65039
Hanke, Martin; Nagy, James; Plemmons, Robert
1993
Regularizing properties of a truncated Newton-cg algorithm for nonlinear inverse problems. Zbl 0899.65038
Hanke, Martin
1997
Nonstationary iterated Tikhonov regularization. Zbl 0910.47005
Hanke, M.; Groetsch, C. W.
1998
Accelerated Landweber iterations for the solution of ill-posed equations. Zbl 0745.65038
Hanke, Martin
1991
Limitations of the $$L$$-curve method in ill-posed problems. Zbl 0849.65039
Hanke, Martin
1996
Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques. Zbl 0859.65141
Hanke, Martin; Nagy, James G.
1996
A general heuristic for choosing the regularization parameter in ill-posed problems. Zbl 0859.65051
Hanke, Martin; Raus, Toomas
1996
Recent progress in electrical impedance tomography. Zbl 1048.92022
Hanke, Martin; Brühl, Martin
2003
Error analysis of an equation error method for the identification of the diffusion coefficient in a quasi-linear parabolic differential equation. Zbl 0928.35198
Hanke, Martin; Scherzer, Otmar
1999
Quasi-Newton approach to nonnegative image restorations. Zbl 0960.65071
Hanke, Martin; Nagy, James G.; Vogel, Curtis
2000
On the acceleration of Kaczmarz’s method for inconsistent linear systems. Zbl 0708.65033
Hanke, Martin; Niethammer, Wilhelm
1990
Crack detection using electrostatic measurements. Zbl 0985.35103
Brühl, Martin; Hanke, Martin; Pidcock, Michael
2001
Justification of point electrode models in electrical impedance tomography. Zbl 1219.65126
Hanke, Martin; Harrach, Bastian; Hyvönen, Nuutti
2011
Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurring. Zbl 1285.65030
Donatelli, Marco; Hanke, Martin
2013
The regularizing Levenberg-Marquardt scheme is of optimal order. Zbl 1204.65059
Hanke, Martin
2010
Preconditionings and splittings for rectangular systems. Zbl 0704.65018
Hanke, Martin; Neumann, Michael
1990
Two-level preconditioners for regularized inverse problems. I: Theory. Zbl 0941.65056
Hanke, Martin; Vogel, Curtis R.
1999
Identification of small inhomogeneities asymptotic factorization. Zbl 1119.35111
Ammari, Habib; Griesmaier, Roland; Hanke, Martin
2007
Fast preconditioned conjugate gradient algorithms for Wiener-Hopf integral equations. Zbl 0820.65092
Gohberg, I.; Hanke, M.; Koltracht, I.
1994
A Chebyshev-like semiiteration for inconsistent linear systems. Zbl 0809.65039
Hanke, Martin; Hochbruck, Marlis
1993
On rational approximation methods for inverse source problems. Zbl 1215.35166
Hanke, Martin; Rundell, William
2011
Deblurring methods using antireflective boundary conditions. Zbl 1167.65361
Christiansen, Martin; Hanke, Martin
2008
Far field splitting for the Helmholtz equation. Zbl 1295.35381
Griesmaier, Roland; Hanke, Martin; Sylvester, John
2014
Inverse Toeplitz preconditioners for ill-posed problems. Zbl 0935.65037
Hanke, Martin; Nagy, James
1998
Inverse source problems for the Helmholtz equation and the windowed Fourier transform. Zbl 1251.35187
Griesmaier, Roland; Hanke, Martin; Raasch, Thorsten
2012
Inverse source problems for the Helmholtz equation and the windowed Fourier transform. II. Zbl 1282.35412
Griesmaier, Roland; Hanke, Martin; Raasch, Thorsten
2013
The factorization method for electrical impedance tomography in the half-space. Zbl 1151.65085
Hanke, Martin; Schappel, Birgit
2008
Regularization methods for constrained mechanical multibody systems. Zbl 0888.70014
Eich, E.; Hanke, M.
1995
Highly accurate finite element method for one-dimensional elliptic interface problems. Zbl 1181.65109
Loubenets, A.; Ali, T.; Hanke, M.
2009
A sampling method for detecting buried objects using electromagnetic scattering. Zbl 1112.78013
Gebauer, Bastian; Hanke, Martin; Kirsch, Andreas; Muniz, Wagner; Schneider, Christoph
2005
On the Landweber iteration for nonlinear ill-posed problems. Zbl 0879.65037
Binder, A.; Hanke, M.; Scherzer, O.
1996
Convex backscattering support in electric impedance tomography. Zbl 1215.78011
Hanke, Martin; Hyvönen, Nuutti; Reusswig, Stefanie
2011
Sampling methods. Zbl 1259.35222
Hanke, Martin; Kirsch, Andreas
2011
On real-time algorithms for the location search of discontinuous conductivities with one measurement. Zbl 1153.35403
Hanke, Martin
2008
Convex source support and its application to electric impedance tomography. Zbl 1179.35345
Hanke, Martin; Hyvönen, Nuutti; Reusswig, Stefanie
2008
Regularization with differential operators: An iterative approach. Zbl 0769.65027
Hanke, Martin
1992
Foundations of numerical mathematics and scientific computing. 3rd revised ed. (Grundlagen der numerischen Mathematik und des wissenschaftlichen Rechnens.) Zbl 1155.65001
Hanke-Bourgeois, Martin
2009
Sampling methods. 2nd edition. Zbl 1331.35385
Hanke-Bourgeois, Martin; Kirsch, Andreas
2015
A taste of inverse problems. Basic theory and examples. Zbl 1381.65042
Hanke, Martin
2017
The minimal error conjugate gradient method is a regularization method. Zbl 0851.65033
Hanke, Martin
1995
A note on conjugate-gradient type methods for indefinite and/or inconsistent linear systems. Zbl 0847.65018
Fischer, Bernd; Hanke, Martin; Hochbruck, Marlis
1996
Toeplitz approximate inverse preconditioner for banded Toeplitz matrices. Zbl 0810.65029
Hanke, Martin; Nagy, James G.
1994
On the use of small relaxation parameters in Kaczmarz’s method. Zbl 0716.65040
Hanke, M.; Niethammer, W.
1990
Multifrequency impedance imaging with multiple signal classification. Zbl 1432.94014
Griesmaier, Roland; Hanke, Martin
2015
An inverse backscatter problem for electric impedance tomography. Zbl 1197.35321
Hanke, Martin; Hyvönen, Nuutti; Reusswig, Stefanie
2009
On the condition number of the antireflective transform. Zbl 1181.94041
Donatelli, Marco; Hanke, Martin
2010
Asymptotic expansions for regularization methods of linear fully implicit differential-algebraic equations. Zbl 0805.34002
Hanke, M.
1994
One shot inverse scattering via rational approximation. Zbl 1248.35233
Hanke, Martin
2012
A note on the nonlinear Landweber iteration. Zbl 1307.65078
Hanke, Martin
2014
Why linear sampling really seems to work. Zbl 1180.35560
Hanke, Martin
2008
Computation of local volatilities from regularized Dupire equations. Zbl 1100.91044
Hanke, Martin; Rösler, Elisabeth
2005
A note on Tikhonov regularization of large linear problems. Zbl 1043.65064
Hanke, Martin
2003
The geometry of the set of scaled projections. Zbl 0782.15002
Hanke, Martin
1993
Well-posedness of the iterative Boltzmann inversion. Zbl 1390.82022
Hanke, Martin
2018
Surface reactions on the cytoplasmatic membranes – mathematical modeling of reaction and diffusion systems in a cell. Zbl 1301.92022
Chaudhry, Q. A.; Hanke, M.; Morgenstern, R.; Dreij, K.
2014
Locating several small inclusions in impedance tomography from backscatter data. Zbl 1233.35203
Hanke, Martin
2011
An optimal stopping rule for the $$v$$-method for solving ill-posed problems, using Christoffel functions. Zbl 0812.41028
Hanke, Martin; Engl, Heinz W.
1994
Strong changes of state in collapsing bubbles. Zbl 0925.76858
Hanke, M.; Ballmann, J.
1998
Sampling methods for low-frequency electromagnetic imaging. Zbl 1137.78315
Gebauer, Bastian; Hanke, Martin; Schneider, Christoph
2008
Source supports in electrostatics. Zbl 1152.35111
Hanke, Martin; Hyvönen, Nuutti; Lehn, Manfred; Reusswig, Stefanie
2008
Iterative regularization techniques in image reconstruction. Zbl 0972.65123
Hanke, Martin
2000
Kernel polynomials for the solution of indefinite and ill-posed problems. Zbl 0996.65057
Frankenberger, Harald; Hanke, Martin
2000
Foundations of numerical mathematics and scientific computing. (Grundlagen der numerischen Mathematik und des wissenschaftlichen Rechnens.) Zbl 1010.65001
Hanke-Bourgeois, Martin
2002
A general framework for regularized evaluation of unstable operators. Zbl 0887.47013
Groetsch, Charles W.; Hanke, Martin
1996
MUSIC-characterization of small scatterers for normal measurement data. Zbl 1167.35542
Griesmaier, Roland; Hanke, Martin
2009
Fréchet differentiability of molecular distribution functions. I: $$L^\infty$$ analysis. Zbl 1383.82010
Hanke, Martin
2018
An $$\epsilon$$-free a posteriori stopping rule for certain iterative regularization methods. Zbl 0783.65051
Hanke, Martin
1993
An asymptotic factorization method for inverse electromagnetic scattering in layered media. II: A numerical study. Zbl 1179.78063
Griesmaier, Roland; Hanke, Martin
2009
A note on the MUSIC algorithm for impedance tomography. Zbl 06691652
Hanke, Martin
2017
Regularization by projection for unbounded operators arising in inverse problems. Zbl 0823.65053
Groetsch, C. W.; Hanke, Martin
1995
Superlinear convergence rates for the Lanczos method applied to elliptic operators. Zbl 0887.65055
Hanke, Martin
1997
A note on the uniqueness result for the inverse Henderson problem. Zbl 1422.82018
Frommer, F.; Hanke, M.; Jansen, S.
2019
Fréchet differentiability of molecular distribution functions. II: The Ursell function. Zbl 1383.82011
Hanke, Martin
2018
Foundations of numerical mathematics and scientific computing. 2nd revised and expanded ed. (Grundlagen der numerischen Mathematik und des wissenschaftlichen Rechnens.) Zbl 1109.65001
Hanke-Bourgeois, Martin
2006
Iterative Lösung gewichteter linearer Ausgleichsprobleme. (Iterative solution of weighted linear adjustment problems). Zbl 0694.65014
Hanke, Martin
1989
Unique solvability of a system of ordinary differential equations modeling a warm cloud parcel. Zbl 1437.37113
Hanke, Martin; Porz, Nikolas
2020
Asymptotics of orthogonal polynomials and the numerical solution of ill-posed problems. Zbl 0851.65035
Hanke, Martin
1996
Convex source support in three dimensions. Zbl 1238.65108
Hanke, Martin; Harhanen, Lauri; Hyvönen, Nuutti; Schweickert, Eva
2012
A second look at Nemirovskii’s analysis of the conjugate gradient method. Zbl 0810.65047
Hanke, M.
1994
Unique solvability of a system of ordinary differential equations modeling a warm cloud parcel. Zbl 1437.37113
Hanke, Martin; Porz, Nikolas
2020
A note on the uniqueness result for the inverse Henderson problem. Zbl 1422.82018
Frommer, F.; Hanke, M.; Jansen, S.
2019
Well-posedness of the iterative Boltzmann inversion. Zbl 1390.82022
Hanke, Martin
2018
Fréchet differentiability of molecular distribution functions. I: $$L^\infty$$ analysis. Zbl 1383.82010
Hanke, Martin
2018
Fréchet differentiability of molecular distribution functions. II: The Ursell function. Zbl 1383.82011
Hanke, Martin
2018
A taste of inverse problems. Basic theory and examples. Zbl 1381.65042
Hanke, Martin
2017
A note on the MUSIC algorithm for impedance tomography. Zbl 06691652
Hanke, Martin
2017
Sampling methods. 2nd edition. Zbl 1331.35385
Hanke-Bourgeois, Martin; Kirsch, Andreas
2015
Multifrequency impedance imaging with multiple signal classification. Zbl 1432.94014
Griesmaier, Roland; Hanke, Martin
2015
Far field splitting for the Helmholtz equation. Zbl 1295.35381
Griesmaier, Roland; Hanke, Martin; Sylvester, John
2014
A note on the nonlinear Landweber iteration. Zbl 1307.65078
Hanke, Martin
2014
Surface reactions on the cytoplasmatic membranes – mathematical modeling of reaction and diffusion systems in a cell. Zbl 1301.92022
Chaudhry, Q. A.; Hanke, M.; Morgenstern, R.; Dreij, K.
2014
Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurring. Zbl 1285.65030
Donatelli, Marco; Hanke, Martin
2013
Inverse source problems for the Helmholtz equation and the windowed Fourier transform. II. Zbl 1282.35412
Griesmaier, Roland; Hanke, Martin; Raasch, Thorsten
2013
Inverse source problems for the Helmholtz equation and the windowed Fourier transform. Zbl 1251.35187
Griesmaier, Roland; Hanke, Martin; Raasch, Thorsten
2012
One shot inverse scattering via rational approximation. Zbl 1248.35233
Hanke, Martin
2012
Convex source support in three dimensions. Zbl 1238.65108
Hanke, Martin; Harhanen, Lauri; Hyvönen, Nuutti; Schweickert, Eva
2012
Justification of point electrode models in electrical impedance tomography. Zbl 1219.65126
Hanke, Martin; Harrach, Bastian; Hyvönen, Nuutti
2011
On rational approximation methods for inverse source problems. Zbl 1215.35166
Hanke, Martin; Rundell, William
2011
Convex backscattering support in electric impedance tomography. Zbl 1215.78011
Hanke, Martin; Hyvönen, Nuutti; Reusswig, Stefanie
2011
Sampling methods. Zbl 1259.35222
Hanke, Martin; Kirsch, Andreas
2011
Locating several small inclusions in impedance tomography from backscatter data. Zbl 1233.35203
Hanke, Martin
2011
The regularizing Levenberg-Marquardt scheme is of optimal order. Zbl 1204.65059
Hanke, Martin
2010
On the condition number of the antireflective transform. Zbl 1181.94041
Donatelli, Marco; Hanke, Martin
2010
Highly accurate finite element method for one-dimensional elliptic interface problems. Zbl 1181.65109
Loubenets, A.; Ali, T.; Hanke, M.
2009
Foundations of numerical mathematics and scientific computing. 3rd revised ed. (Grundlagen der numerischen Mathematik und des wissenschaftlichen Rechnens.) Zbl 1155.65001
Hanke-Bourgeois, Martin
2009
An inverse backscatter problem for electric impedance tomography. Zbl 1197.35321
Hanke, Martin; Hyvönen, Nuutti; Reusswig, Stefanie
2009
MUSIC-characterization of small scatterers for normal measurement data. Zbl 1167.35542
Griesmaier, Roland; Hanke, Martin
2009
An asymptotic factorization method for inverse electromagnetic scattering in layered media. II: A numerical study. Zbl 1179.78063
Griesmaier, Roland; Hanke, Martin
2009
Deblurring methods using antireflective boundary conditions. Zbl 1167.65361
Christiansen, Martin; Hanke, Martin
2008
The factorization method for electrical impedance tomography in the half-space. Zbl 1151.65085
Hanke, Martin; Schappel, Birgit
2008
On real-time algorithms for the location search of discontinuous conductivities with one measurement. Zbl 1153.35403
Hanke, Martin
2008
Convex source support and its application to electric impedance tomography. Zbl 1179.35345
Hanke, Martin; Hyvönen, Nuutti; Reusswig, Stefanie
2008
Why linear sampling really seems to work. Zbl 1180.35560
Hanke, Martin
2008
Sampling methods for low-frequency electromagnetic imaging. Zbl 1137.78315
Gebauer, Bastian; Hanke, Martin; Schneider, Christoph
2008
Source supports in electrostatics. Zbl 1152.35111
Hanke, Martin; Hyvönen, Nuutti; Lehn, Manfred; Reusswig, Stefanie
2008
Identification of small inhomogeneities asymptotic factorization. Zbl 1119.35111
Ammari, Habib; Griesmaier, Roland; Hanke, Martin
2007
Foundations of numerical mathematics and scientific computing. 2nd revised and expanded ed. (Grundlagen der numerischen Mathematik und des wissenschaftlichen Rechnens.) Zbl 1109.65001
Hanke-Bourgeois, Martin
2006
A sampling method for detecting buried objects using electromagnetic scattering. Zbl 1112.78013
Gebauer, Bastian; Hanke, Martin; Kirsch, Andreas; Muniz, Wagner; Schneider, Christoph
2005
Computation of local volatilities from regularized Dupire equations. Zbl 1100.91044
Hanke, Martin; Rösler, Elisabeth
2005
A direct impedance tomography algorithm for locating small inhomogeneities. Zbl 1016.65079
Brühl, Martin; Hanke, Martin; Vogelius, Michael S.
2003
Recent progress in electrical impedance tomography. Zbl 1048.92022
Hanke, Martin; Brühl, Martin
2003
A note on Tikhonov regularization of large linear problems. Zbl 1043.65064
Hanke, Martin
2003
Foundations of numerical mathematics and scientific computing. (Grundlagen der numerischen Mathematik und des wissenschaftlichen Rechnens.) Zbl 1010.65001
Hanke-Bourgeois, Martin
2002
Inverse problems light: Numerical differentiation. Zbl 1002.65029
Hanke, Martin; Scherzer, Otmar
2001
Crack detection using electrostatic measurements. Zbl 0985.35103
Brühl, Martin; Hanke, Martin; Pidcock, Michael
2001
Numerical implementation of two noniterative methods for locating inclusions by impedance tomography. Zbl 0955.35076
Brühl, Martin; Hanke, Martin
2000
Quasi-Newton approach to nonnegative image restorations. Zbl 0960.65071
Hanke, Martin; Nagy, James G.; Vogel, Curtis
2000
Iterative regularization techniques in image reconstruction. Zbl 0972.65123
Hanke, Martin
2000
Kernel polynomials for the solution of indefinite and ill-posed problems. Zbl 0996.65057
Frankenberger, Harald; Hanke, Martin
2000
Error analysis of an equation error method for the identification of the diffusion coefficient in a quasi-linear parabolic differential equation. Zbl 0928.35198
Hanke, Martin; Scherzer, Otmar
1999
Two-level preconditioners for regularized inverse problems. I: Theory. Zbl 0941.65056
Hanke, Martin; Vogel, Curtis R.
1999
Nonstationary iterated Tikhonov regularization. Zbl 0910.47005
Hanke, M.; Groetsch, C. W.
1998
Inverse Toeplitz preconditioners for ill-posed problems. Zbl 0935.65037
Hanke, Martin; Nagy, James
1998
Strong changes of state in collapsing bubbles. Zbl 0925.76858
Hanke, M.; Ballmann, J.
1998
A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems. Zbl 0873.65057
Hanke, Martin
1997
Regularizing properties of a truncated Newton-cg algorithm for nonlinear inverse problems. Zbl 0899.65038
Hanke, Martin
1997
Superlinear convergence rates for the Lanczos method applied to elliptic operators. Zbl 0887.65055
Hanke, Martin
1997
Regularization of inverse problems. Zbl 0859.65054
Engl, Heinz W.; Hanke, Martin; Neubauer, Andreas
1996
Limitations of the $$L$$-curve method in ill-posed problems. Zbl 0849.65039
Hanke, Martin
1996
Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques. Zbl 0859.65141
Hanke, Martin; Nagy, James G.
1996
A general heuristic for choosing the regularization parameter in ill-posed problems. Zbl 0859.65051
Hanke, Martin; Raus, Toomas
1996
On the Landweber iteration for nonlinear ill-posed problems. Zbl 0879.65037
Binder, A.; Hanke, M.; Scherzer, O.
1996
A note on conjugate-gradient type methods for indefinite and/or inconsistent linear systems. Zbl 0847.65018
Fischer, Bernd; Hanke, Martin; Hochbruck, Marlis
1996
A general framework for regularized evaluation of unstable operators. Zbl 0887.47013
Groetsch, Charles W.; Hanke, Martin
1996
Asymptotics of orthogonal polynomials and the numerical solution of ill-posed problems. Zbl 0851.65035
Hanke, Martin
1996
A convergence analysis of the Landweber iteration for nonlinear ill-posed problems. Zbl 0840.65049
Hanke, Martin; Neubauer, Andreas; Scherzer, Otmar
1995
Conjugate gradient type methods for ill-posed problems. Zbl 0830.65043
Hanke, Martin
1995
Regularization methods for constrained mechanical multibody systems. Zbl 0888.70014
Eich, E.; Hanke, M.
1995
The minimal error conjugate gradient method is a regularization method. Zbl 0851.65033
Hanke, Martin
1995
Regularization by projection for unbounded operators arising in inverse problems. Zbl 0823.65053
Groetsch, C. W.; Hanke, Martin
1995
Fast preconditioned conjugate gradient algorithms for Wiener-Hopf integral equations. Zbl 0820.65092
Gohberg, I.; Hanke, M.; Koltracht, I.
1994
Toeplitz approximate inverse preconditioner for banded Toeplitz matrices. Zbl 0810.65029
Hanke, Martin; Nagy, James G.
1994
Asymptotic expansions for regularization methods of linear fully implicit differential-algebraic equations. Zbl 0805.34002
Hanke, M.
1994
An optimal stopping rule for the $$v$$-method for solving ill-posed problems, using Christoffel functions. Zbl 0812.41028
Hanke, Martin; Engl, Heinz W.
1994
A second look at Nemirovskii’s analysis of the conjugate gradient method. Zbl 0810.65047
Hanke, M.
1994
Regularization methods for large-scale problems. Zbl 0805.65058
Hanke, Martin; Hansen, Per Christian
1993
Preconditioned iterative regularization for ill-posed problems. Zbl 0794.65039
Hanke, Martin; Nagy, James; Plemmons, Robert
1993
A Chebyshev-like semiiteration for inconsistent linear systems. Zbl 0809.65039
Hanke, Martin; Hochbruck, Marlis
1993
The geometry of the set of scaled projections. Zbl 0782.15002
Hanke, Martin
1993
An $$\epsilon$$-free a posteriori stopping rule for certain iterative regularization methods. Zbl 0783.65051
Hanke, Martin
1993
Regularization with differential operators: An iterative approach. Zbl 0769.65027
Hanke, Martin
1992
Accelerated Landweber iterations for the solution of ill-posed equations. Zbl 0745.65038
Hanke, Martin
1991
Tikhonov regularization of nonlinear differential-algebraic equations. Zbl 0711.34018
Engl, H. W.; Hanke, M.; Neubauer, A.
1990
On the acceleration of Kaczmarz’s method for inconsistent linear systems. Zbl 0708.65033
Hanke, Martin; Niethammer, Wilhelm
1990
Preconditionings and splittings for rectangular systems. Zbl 0704.65018
Hanke, Martin; Neumann, Michael
1990
On the use of small relaxation parameters in Kaczmarz’s method. Zbl 0716.65040
Hanke, M.; Niethammer, W.
1990
Iterative Lösung gewichteter linearer Ausgleichsprobleme. (Iterative solution of weighted linear adjustment problems). Zbl 0694.65014
Hanke, Martin
1989
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### Cited by 2,394 Authors

 78 Reichel, Lothar 31 Han, Bo 30 Hofmann, Bernd 30 Kaltenbacher, Barbara 29 Hanke-Bourgeois, Martin 27 Xiong, Xiangtuan 25 Donatelli, Marco 25 Fu, Chuli 25 Wei, Ting 24 Jin, Qinian 21 Kindermann, Stefan 21 Ramlau, Ronny 20 Scherzer, Otmar 19 Buccini, Alessandro 19 Nair, M. Thamban 18 Hyvönen, Nuutti 18 Jin, Bangti 18 Neubauer, Andreas 17 Ammari, Habib M. 17 Lu, Shuai 17 Serra-Capizzano, Stefano 17 Yang, Liu 16 Deng, Zuicha 16 Hasanoǧlu, Alemdar 16 Mathé, Peter 16 Sgallari, Fiorella 15 George, Santhosh 15 Marin, Liviu 15 Wei, Yimin 14 Harrach, Bastian 14 Leonov, Aleksandr Sergeevich 14 Morigi, Serena 13 Hohage, Thorsten 13 Jbilou, Khalide 13 Leitão, Antonio 13 Pereverzev, Sergei V. 13 Zou, Jun 12 Burger, Martin 12 Griesmaier, Roland 12 Lesnic, Daniel 12 Nagy, James Gerard 12 Qian, Zhi 11 He, Guoqiang 11 Kang, Hyeonbae 11 Landi, Germana 11 Loli Piccolomini, Elena 11 Stuart, Andrew M. 10 Chung, Julianne M. 10 Estatico, Claudio 10 Haltmeier, Markus 10 Mahale, Pallavi 10 Needell, Deanna 10 Smirnova, Alexandra B. 10 Tautenhahn, Ulrich 10 Viloche Bazán, Fermín S. 10 Wang, Wei 10 Zhang, Ye 9 Bakushinskĭ, Anatoliĭ Borisovich B. 9 Bouhamidi, Abderrahman 9 Calvetti, Daniela 9 Gerth, Daniel 9 Hansen, Per Christian 9 Li, Xiaoxiao 9 Maass, Peter 9 Novati, Paolo 9 Rodriguez, Giuseppe 9 Yang, Fan 9 Zhang, Yuanxiang 9 Zhao, Zhenyu 8 Ascher, Uri M. 8 Blanchard, Gilles 8 Cheng, Xiaoliang 8 De Cezaro, Adriano 8 Đinh Nho Hào 8 Feng, Xiaoli 8 Garde, Henrik 8 Golubev, Yuriĭ K. 8 Hämarik, Uno 8 Huang, Ting-Zhu 8 Iglesias, Marco A. 8 Klibanov, Michael V. 8 Loubes, Jean-Michel 8 Meng, Zehong 8 Noschese, Silvia 8 Rajan, M. P. 8 Rosasco, Lorenzo A. 8 Sadok, Hassane 8 Tong, Shanshan 8 Yang, Hongqi 8 Zama, Fabiana 7 Cheng, Hao 7 Cheng, Jin 7 Egger, Herbert 7 Favati, Paola 7 Gazzola, Silvia 7 Huang, Guang-Xin 7 Jia, Zhongxiao 7 Knudsen, Kim M. 7 Kress, Rainer 7 Liu, Ji-Chuan ...and 2,294 more Authors
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### Cited in 300 Serials

 128 Journal of Computational and Applied Mathematics 125 Inverse Problems 97 Journal of Inverse and Ill-Posed Problems 87 Applied Mathematics and Computation 65 Inverse Problems in Science and Engineering 51 Applied Numerical Mathematics 49 Inverse Problems and Imaging 46 Numerical Algorithms 44 Linear Algebra and its Applications 43 Numerische Mathematik 35 Journal of Computational Physics 34 Numerical Functional Analysis and Optimization 32 SIAM Journal on Scientific Computing 32 SIAM Journal on Imaging Sciences 30 BIT 29 Computers & Mathematics with Applications 28 Mathematics of Computation 28 Journal of Integral Equations and Applications 26 Applicable Analysis 26 Applied Mathematical Modelling 25 Journal of Mathematical Analysis and Applications 22 SIAM Journal on Applied Mathematics 19 Mathematics and Computers in Simulation 18 Journal of Scientific Computing 18 Engineering Analysis with Boundary Elements 17 SIAM Journal on Numerical Analysis 16 International Journal of Computer Mathematics 16 Journal of Mathematical Imaging and Vision 16 ETNA. Electronic Transactions on Numerical Analysis 15 Computer Methods in Applied Mechanics and Engineering 15 Journal of Optimization Theory and Applications 15 Advances in Computational Mathematics 13 Calcolo 13 SIAM Journal on Matrix Analysis and Applications 13 Computational Optimization and Applications 12 Electronic Journal of Statistics 11 Computational Mathematics and Mathematical Physics 11 Numerical Linear Algebra with Applications 11 Computational Geosciences 11 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Mathematical Methods in the Applied Sciences 10 Computational and Applied Mathematics 10 Mathematical Problems in Engineering 10 Computational Methods in Applied Mathematics 9 Applied Mathematics Letters 9 SIAM Journal on Mathematical Analysis 9 Applied and Computational Harmonic Analysis 9 Journal of Applied Mathematics and Computing 9 GEM - International Journal on Geomathematics 8 Journal of Engineering Mathematics 8 Zeitschrift für Analysis und ihre Anwendungen 8 International Journal of Computational Methods 7 The Annals of Statistics 7 Mathematical and Computer Modelling 7 Russian Mathematics 7 The Journal of Fourier Analysis and Applications 7 Abstract and Applied Analysis 7 Communications in Nonlinear Science and Numerical Simulation 7 Multiscale Modeling & Simulation 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Acta Mathematicae Applicatae Sinica. English Series 6 SIAM Journal on Optimization 6 Mathematical Methods of Statistics 6 Journal of Mathematical Sciences (New York) 6 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Journal of Shanghai University 6 Foundations of Computational Mathematics 6 Journal of Machine Learning Research (JMLR) 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Computer Physics Communications 5 Journal of Mathematical Biology 5 Journal of Complexity 5 Computational Mechanics 5 Bernoulli 5 Journal of Inequalities and Applications 5 Optimization and Engineering 5 Analysis and Applications (Singapore) 5 SIAM/ASA Journal on Uncertainty Quantification 5 AIMS Mathematics 4 International Journal of Heat and Mass Transfer 4 Journal of Mathematical Physics 4 Applied Mathematics and Optimization 4 Computing 4 Integral Equations and Operator Theory 4 Proceedings of the American Mathematical Society 4 Applied Mathematics and Mechanics. (English Edition) 4 Chinese Annals of Mathematics. Series B 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Communications in Statistics. Theory and Methods 4 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 4 Filomat 4 Journal of Mathematical Chemistry 4 Nonlinear Analysis. Real World Applications 4 Journal of Applied Mathematics 4 East Asian Journal on Applied Mathematics 3 International Journal of Solids and Structures 3 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 3 Mathematical Biosciences 3 Bulletin of Mathematical Biology 3 International Journal for Numerical Methods in Engineering ...and 200 more Serials
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### Cited in 52 Fields

 1,474 Numerical analysis (65-XX) 649 Partial differential equations (35-XX) 388 Operator theory (47-XX) 183 Calculus of variations and optimal control; optimization (49-XX) 177 Statistics (62-XX) 173 Information and communication theory, circuits (94-XX) 143 Integral equations (45-XX) 140 Biology and other natural sciences (92-XX) 138 Optics, electromagnetic theory (78-XX) 121 Operations research, mathematical programming (90-XX) 119 Computer science (68-XX) 74 Mechanics of deformable solids (74-XX) 69 Linear and multilinear algebra; matrix theory (15-XX) 63 Fluid mechanics (76-XX) 52 Classical thermodynamics, heat transfer (80-XX) 48 Geophysics (86-XX) 45 Probability theory and stochastic processes (60-XX) 41 Systems theory; control (93-XX) 31 Ordinary differential equations (34-XX) 28 Functional analysis (46-XX) 27 Integral transforms, operational calculus (44-XX) 24 Approximations and expansions (41-XX) 24 Harmonic analysis on Euclidean spaces (42-XX) 21 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 19 Real functions (26-XX) 17 Functions of a complex variable (30-XX) 16 Potential theory (31-XX) 16 Statistical mechanics, structure of matter (82-XX) 10 Dynamical systems and ergodic theory (37-XX) 7 Global analysis, analysis on manifolds (58-XX) 7 Quantum theory (81-XX) 6 Combinatorics (05-XX) 6 Special functions (33-XX) 6 Convex and discrete geometry (52-XX) 5 General and overarching topics; collections (00-XX) 5 Differential geometry (53-XX) 4 Difference and functional equations (39-XX) 4 Mechanics of particles and systems (70-XX) 3 Astronomy and astrophysics (85-XX) 3 Mathematics education (97-XX) 2 Measure and integration (28-XX) 2 Sequences, series, summability (40-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Abstract harmonic analysis (43-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) 1 Relativity and gravitational theory (83-XX)