# zbMATH — the first resource for mathematics

## Rieder, Andreas

Compute Distance To:
 Author ID: rieder.andreas Published as: Rieder, A.; Rieder, Andreas
 Documents Indexed: 59 Publications since 1989, including 6 Books
all top 5

#### Co-Authors

 15 single-authored 6 Schuster, Thomas 5 Kirsch, Andreas 4 Louis, Alfred Karl 4 Maass, Peter 4 Quinto, Eric Todd 3 Grathwohl, Christine 3 Kunstmann, Peer Christian 3 Lechleiter, Armin 3 Wells, Raymond O. jun. 3 Zhou, Xiaodong 2 Glowinski, Roland 2 Margotti, Fábio 2 Winkler, Robert L. 1 Brunk, Jochen 1 Dietz, Rainer 1 Dörfler, Willy 1 Faridani, Adel 1 Hochbruck, Marlis 1 Hundertmark, Dirk 1 Kreutzmann, Tim 1 Leitão, Antonio 1 Morgner, Uwe 1 Reichel, Wolfgang 1 Schnaubelt, Roland 1 Schneck, Arne 1 Schöpfer, Frank 1 Schörkhuber, Birgit
all top 5

#### Serials

 11 Inverse Problems 7 Numerische Mathematik 4 SIAM Journal on Numerical Analysis 2 Mathematical Methods in the Applied Sciences 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 SIAM Journal on Applied Mathematics 2 SIAM Journal on Imaging Sciences 1 Applicable Analysis 1 Mathematics of Computation 1 Applied and Computational Harmonic Analysis 1 Annales Universitatis Saraviensis. Series Mathematicae 1 Journal of Inverse and Ill-Posed Problems 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Inverse Problems and Imaging 1 PAMM. Proceedings in Applied Mathematics and Mechanics 1 Trends in Mathematics
all top 5

#### Fields

 39 Numerical analysis (65-XX) 19 Partial differential equations (35-XX) 16 Integral transforms, operational calculus (44-XX) 13 Operator theory (47-XX) 9 Biology and other natural sciences (92-XX) 6 Geophysics (86-XX) 4 Information and communication theory, circuits (94-XX) 3 General and overarching topics; collections (00-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Integral equations (45-XX) 3 Computer science (68-XX) 3 Optics, electromagnetic theory (78-XX) 2 Ordinary differential equations (34-XX) 1 Mechanics of deformable solids (74-XX)

#### Citations contained in zbMATH Open

42 Publications have been cited 342 times in 246 Documents Cited by Year
On the regularization of nonlinear ill-posed problems via inexact Newton iterations. Zbl 0969.65049
Rieder, Andreas
1999
No problems with inverse problems. An introduction to its stable solutions. Zbl 1057.65035
Rieder, Andreas
2003
On convergence rates of inexact Newton regularizations. Zbl 0990.65061
Rieder, Andreas
2001
Wavelets. Theory and applications. Zbl 0897.42019
Louis, Alfred Karl; Maaß, Peter; Rieder, Andreas
1997
A wavelet multilevel method for ill-posed problems stabilized by Tikhonov regularization. Zbl 0878.65039
Rieder, Andreas
1997
Local inversion of the sonar transform regularized by the approximate inverse. Zbl 1214.65066
Quinto, Eric Todd; Rieder, Andreas; Schuster, Thomas
2011
Newton regularizations for impedance tomography: Convergence by local injectivity. Zbl 1152.35516
Lechleiter, Armin; Rieder, Andreas
2008
Inexact Newton regularization using conjugate gradients as inner iteration. Zbl 1092.65047
Rieder, Andreas
2005
The approximate inverse in action with an application to computerized tomography. Zbl 0961.65112
Rieder, Andreas; Schuster, Thomas
2000
Newton regularizations for impedance tomography: a numerical study. Zbl 1109.65100
Lechleiter, Armin; Rieder, Andreas
2006
Towards a general convergence theory for inexact Newton regularizations. Zbl 1201.65090
Lechleiter, Armin; Rieder, Andreas
2010
A Kaczmarz version of the REGINN-Landweber iteration for ill-posed problems in Banach spaces. Zbl 1320.65087
Margotti, Fábio; Rieder, Andreas; Leitão, Antonio
2014
The approximate inverse in action II: convergence and stability. Zbl 1022.65066
Rieder, Andreas; Schuster, Thomas
2003
The approximate inverse in action. III: 3D-Doppler tomography. Zbl 1071.65178
Rieder, Andreas; Schuster, Thomas
2004
Resolution-controlled conductivity discretization in electrical impedance tomography. Zbl 1309.65130
Winkler, Robert; Rieder, Andreas
2014
Runge-Kutta integrators yield optimal regularization schemes. Zbl 1075.65078
Rieder, Andreas
2005
Inverse problems for abstract evolution equations with applications in electrodynamics and elasticity. Zbl 1416.65164
Kirsch, Andreas; Rieder, Andreas
2016
An inexact Newton regularization in Banach spaces based on the nonstationary iterated Tikhonov method. Zbl 1321.65091
Margotti, Fábio; Rieder, Andreas
2015
On the linearization of operators related to the full waveform inversion in seismology. Zbl 1319.35300
Kirsch, Andreas; Rieder, Andreas
2014
Incomplete data problems in X-ray computerized tomography. II: Truncated projections and region-of-interest tomography. Zbl 0675.65137
Louis, Alfred K.; Rieder, Andreas
1989
The wavelet transform on Sobolev spaces and its approximation properties. Zbl 0699.44003
Rieder, Andreas
1991
Optimality of the fully discrete filtered backprojection algorithm for tomographic inversion. Zbl 1131.65104
Rieder, Andreas; Schneck, Arne
2007
The semidiscrete filtered backprojection algorithm is optimal for tomographic inversion. Zbl 1052.65118
2003
Wavelet-accelerated Tikhonov-Phillips regularization with applications. Zbl 0880.65028
Maaß, Peter; Rieder, Andreas
1997
Approximate inverse for the common offset acquisition geometry in 2D seismic imaging. Zbl 1404.86031
Grathwohl, Christine; Kunstmann, Peer; Quinto, Eric Todd; Rieder, Andreas
2018
A wavelet approach to robust multilevel solvers for anisotropic elliptic problems. Zbl 0864.65073
Rieder, Andreas; Wells, Raymond O. jun.; Zhou, Xiaodong
1994
On the robustness of the damped $$V$$-cycle of the wavelet frequency decomposition multigrid method. Zbl 0809.65118
Rieder, A.; Zhou, X.
1994
Seismic tomography is locally ill-posed. Zbl 1308.86007
Kirsch, Andreas; Rieder, Andreas
2014
Rieder, Andreas
2001
Wavelets. Theory and applications. 2., überarb. und erweiterte Aufl. Zbl 0897.42018
Louis, Alfred Karl; Maaß, Peter; Rieder, Andreas
1998
A preconditioned CG-method for wavelet-Galerkin discretizations of elliptic problems. Zbl 0850.65221
Glowinski, R.; Rieder, A.; Wells, R. O.; Zhou, X.
1995
Wavelets. Theory and applications. Zbl 0845.42011
Louis, Alfred Karl; Maaß, Peter; Rieder, Andreas
1994
Microlocal analysis of imaging operators for effective common offset seismic reconstruction. Zbl 1397.35007
Grathwohl, Christine; Kunstmann, Peer; Quinto, Eric Todd; Rieder, Andreas
2018
Model-aware Newton-type inversion scheme for electrical impedance tomography. Zbl 1316.47049
Winkler, Robert; Rieder, Andreas
2015
A domain embedding method for Dirichlet problems in arbitrary space dimension. Zbl 0913.65099
Rieder, Andreas
1998
A wavelet multigrid preconditioner for Dirichlet boundary value problems in general domains. Zbl 0860.65121
Glowinski, Roland; Rieder, Andreas; Wells, Raymond O. jun.; Zhou, Xiaodong
1996
Inverse problems for abstract evolution equations. II: Higher order differentiability for viscoelasticity. Zbl 1427.35361
Kirsch, Andreas; Rieder, Andreas
2019
Embedding and a priori wavelet-adaptivity for Dirichlet problems. Zbl 0985.65149
Rieder, Andreas
2000
Approximate inverse meets local tomography. Zbl 0966.65109
Rieder, Andreas; Dietz, Rainer; Schuster, Thomas
2000
On embedding techniques for 2nd-order elliptic problems. Zbl 0911.65111
Rieder, Andreas
1997
Multilevel methods based on wavelet decompositions. Zbl 0852.65111
Rieder, A.
1994
The high frequency behaviour of continuous wavelet transforms. Zbl 0838.44004
Rieder, Andreas
1994
Inverse problems for abstract evolution equations. II: Higher order differentiability for viscoelasticity. Zbl 1427.35361
Kirsch, Andreas; Rieder, Andreas
2019
Approximate inverse for the common offset acquisition geometry in 2D seismic imaging. Zbl 1404.86031
Grathwohl, Christine; Kunstmann, Peer; Quinto, Eric Todd; Rieder, Andreas
2018
Microlocal analysis of imaging operators for effective common offset seismic reconstruction. Zbl 1397.35007
Grathwohl, Christine; Kunstmann, Peer; Quinto, Eric Todd; Rieder, Andreas
2018
Inverse problems for abstract evolution equations with applications in electrodynamics and elasticity. Zbl 1416.65164
Kirsch, Andreas; Rieder, Andreas
2016
An inexact Newton regularization in Banach spaces based on the nonstationary iterated Tikhonov method. Zbl 1321.65091
Margotti, Fábio; Rieder, Andreas
2015
Model-aware Newton-type inversion scheme for electrical impedance tomography. Zbl 1316.47049
Winkler, Robert; Rieder, Andreas
2015
A Kaczmarz version of the REGINN-Landweber iteration for ill-posed problems in Banach spaces. Zbl 1320.65087
Margotti, Fábio; Rieder, Andreas; Leitão, Antonio
2014
Resolution-controlled conductivity discretization in electrical impedance tomography. Zbl 1309.65130
Winkler, Robert; Rieder, Andreas
2014
On the linearization of operators related to the full waveform inversion in seismology. Zbl 1319.35300
Kirsch, Andreas; Rieder, Andreas
2014
Seismic tomography is locally ill-posed. Zbl 1308.86007
Kirsch, Andreas; Rieder, Andreas
2014
Local inversion of the sonar transform regularized by the approximate inverse. Zbl 1214.65066
Quinto, Eric Todd; Rieder, Andreas; Schuster, Thomas
2011
Towards a general convergence theory for inexact Newton regularizations. Zbl 1201.65090
Lechleiter, Armin; Rieder, Andreas
2010
Newton regularizations for impedance tomography: Convergence by local injectivity. Zbl 1152.35516
Lechleiter, Armin; Rieder, Andreas
2008
Optimality of the fully discrete filtered backprojection algorithm for tomographic inversion. Zbl 1131.65104
Rieder, Andreas; Schneck, Arne
2007
Newton regularizations for impedance tomography: a numerical study. Zbl 1109.65100
Lechleiter, Armin; Rieder, Andreas
2006
Inexact Newton regularization using conjugate gradients as inner iteration. Zbl 1092.65047
Rieder, Andreas
2005
Runge-Kutta integrators yield optimal regularization schemes. Zbl 1075.65078
Rieder, Andreas
2005
The approximate inverse in action. III: 3D-Doppler tomography. Zbl 1071.65178
Rieder, Andreas; Schuster, Thomas
2004
No problems with inverse problems. An introduction to its stable solutions. Zbl 1057.65035
Rieder, Andreas
2003
The approximate inverse in action II: convergence and stability. Zbl 1022.65066
Rieder, Andreas; Schuster, Thomas
2003
The semidiscrete filtered backprojection algorithm is optimal for tomographic inversion. Zbl 1052.65118
2003
On convergence rates of inexact Newton regularizations. Zbl 0990.65061
Rieder, Andreas
2001
Rieder, Andreas
2001
The approximate inverse in action with an application to computerized tomography. Zbl 0961.65112
Rieder, Andreas; Schuster, Thomas
2000
Embedding and a priori wavelet-adaptivity for Dirichlet problems. Zbl 0985.65149
Rieder, Andreas
2000
Approximate inverse meets local tomography. Zbl 0966.65109
Rieder, Andreas; Dietz, Rainer; Schuster, Thomas
2000
On the regularization of nonlinear ill-posed problems via inexact Newton iterations. Zbl 0969.65049
Rieder, Andreas
1999
Wavelets. Theory and applications. 2., überarb. und erweiterte Aufl. Zbl 0897.42018
Louis, Alfred Karl; Maaß, Peter; Rieder, Andreas
1998
A domain embedding method for Dirichlet problems in arbitrary space dimension. Zbl 0913.65099
Rieder, Andreas
1998
Wavelets. Theory and applications. Zbl 0897.42019
Louis, Alfred Karl; Maaß, Peter; Rieder, Andreas
1997
A wavelet multilevel method for ill-posed problems stabilized by Tikhonov regularization. Zbl 0878.65039
Rieder, Andreas
1997
Wavelet-accelerated Tikhonov-Phillips regularization with applications. Zbl 0880.65028
Maaß, Peter; Rieder, Andreas
1997
On embedding techniques for 2nd-order elliptic problems. Zbl 0911.65111
Rieder, Andreas
1997
A wavelet multigrid preconditioner for Dirichlet boundary value problems in general domains. Zbl 0860.65121
Glowinski, Roland; Rieder, Andreas; Wells, Raymond O. jun.; Zhou, Xiaodong
1996
A preconditioned CG-method for wavelet-Galerkin discretizations of elliptic problems. Zbl 0850.65221
Glowinski, R.; Rieder, A.; Wells, R. O.; Zhou, X.
1995
A wavelet approach to robust multilevel solvers for anisotropic elliptic problems. Zbl 0864.65073
Rieder, Andreas; Wells, Raymond O. jun.; Zhou, Xiaodong
1994
On the robustness of the damped $$V$$-cycle of the wavelet frequency decomposition multigrid method. Zbl 0809.65118
Rieder, A.; Zhou, X.
1994
Wavelets. Theory and applications. Zbl 0845.42011
Louis, Alfred Karl; Maaß, Peter; Rieder, Andreas
1994
Multilevel methods based on wavelet decompositions. Zbl 0852.65111
Rieder, A.
1994
The high frequency behaviour of continuous wavelet transforms. Zbl 0838.44004
Rieder, Andreas
1994
The wavelet transform on Sobolev spaces and its approximation properties. Zbl 0699.44003
Rieder, Andreas
1991
Incomplete data problems in X-ray computerized tomography. II: Truncated projections and region-of-interest tomography. Zbl 0675.65137
Louis, Alfred K.; Rieder, Andreas
1989
all top 5

#### Cited by 369 Authors

 13 Rieder, Andreas 10 Quinto, Eric Todd 7 Kaltenbacher, Barbara 7 Schuster, Thomas 7 Slodička, Marián 6 Haltmeier, Markus 6 Hyvönen, Nuutti 6 Jin, Qinian 6 Maass, Peter 5 Hofmann, Bernd 4 Bockmann, Christine 4 Draganescu, Andrei 4 Freeden, Willi 4 Frikel, Jürgen 4 Han, Bo 4 Jin, Bangti 4 Katsevich, Alexander I. 4 Ko, Jeonghwan 4 Kurdila, Andrew J. 4 Lechleiter, Armin 4 Louis, Alfred Karl 4 Nguyen Viet Linh 4 Ramlau, Ronny 4 Svetov, Ivan Evgenyevich 3 Albani, Vinicius V. L. 3 Beckmann, Matthias 3 Grathwohl, Christine 3 Hahn, Bernadette Nadine 3 Harrach, Bastian 3 Kirsch, Andreas 3 Kluth, Tobias 3 Kunstmann, Peer Christian 3 Margotti, Fábio 3 Michel, Volker 3 Nashed, M. Zuhair 3 Neubauer, Andreas 3 Vasilyev, Oleg V. 3 Yang, Hongqi 2 Ambartsoumian, Gaik 2 Bellavia, Stefania 2 Chen, Zhongying 2 Cheng, Sirui 2 Clason, Christian 2 Das, Purna Chandra 2 De Cezaro, Adriano 2 Donatelli, Marco 2 Dorn, Oliver 2 Duits, Remco 2 Felea, Raluca 2 Finěk, Václav 2 Forster-Heinlein, Brigitte 2 Fu, Chuli 2 Fu, Hongsun 2 Garde, Henrik 2 Gehre, Matthias 2 Gerken, Thies 2 Gibson, Peter C. 2 Grote, Marcus J. 2 Guo, Yumeng 2 Hochbruck, Marlis 2 Honig, Michael L. 2 Iske, Armin 2 Jiang, Ming 2 Kazimierski, Kamil S. 2 Kevlahan, Nicholas K.-R. 2 Krishnan, Venkateswaran P. 2 Lal, Shine 2 Leitão, Antonio 2 Leweke, Sarah 2 Li, Housen 2 Luo, Xingjun 2 Maltseva, Svetlana Vasilevna 2 Mustonen, Lauri 2 Nair, M. Thamban 2 Nhu, Vu Huu 2 Nolan, Clifford J. 2 Pereverzyev, Sergiy jun. 2 Pilant, Michael S. 2 Polyakova, Anna Petrovna 2 Prasad, Akhilesh 2 Riccietti, Elisa 2 Sastry, Challa S. 2 Scherzer, Otmar 2 Šeliga, Lukáš 2 Staboulis, Stratos 2 Suchanecki, Zdzislaw 2 Tautenhahn, Ulrich 2 Wald, Anne 2 Zeng, Chunmei 2 Zeng, Li 2 Zhang, Ye 2 Zhang, Yuanxiang 2 Zubelli, Jorge P. 1 Abhishek, Anuj 1 Ahmad, Sanwar 1 Alam, Jahrul M. 1 Alberti, Giovanni S. 1 Altundağ, H. 1 Ammari, Habib M. 1 Andersson, Fredrik K. ...and 269 more Authors
all top 5

#### Cited in 80 Serials

 38 Inverse Problems 20 Journal of Inverse and Ill-Posed Problems 11 Numerische Mathematik 9 Journal of Computational Physics 9 Journal of Computational and Applied Mathematics 9 Inverse Problems in Science and Engineering 7 SIAM Journal on Applied Mathematics 7 Inverse Problems and Imaging 6 Numerical Functional Analysis and Optimization 6 SIAM Journal on Imaging Sciences 5 Mathematics of Computation 5 Applied Mathematics and Computation 4 Journal of Integral Equations and Applications 4 SIAM Journal on Mathematical Analysis 4 Applied and Computational Harmonic Analysis 3 Applicable Analysis 3 Journal of Mathematical Analysis and Applications 3 SIAM Journal on Numerical Analysis 3 Applied Numerical Mathematics 3 Journal of Mathematical Imaging and Vision 3 International Journal of Wavelets, Multiresolution and Information Processing 2 Mathematical Methods in the Applied Sciences 2 BIT 2 Journal of Optimization Theory and Applications 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Computational Mechanics 2 Applied Mathematical Modelling 2 International Journal of Computer Mathematics 2 SIAM Journal on Scientific Computing 2 Journal of Mathematical Sciences (New York) 2 ETNA. Electronic Transactions on Numerical Analysis 2 Advances in Computational Mathematics 2 The Journal of Fourier Analysis and Applications 2 Abstract and Applied Analysis 2 GEM - International Journal on Geomathematics 1 Computer Methods in Applied Mechanics and Engineering 1 Communications on Pure and Applied Mathematics 1 Journal of Mathematical Biology 1 Physics Letters. A 1 Chaos, Solitons and Fractals 1 Calcolo 1 Journal of Approximation Theory 1 Journal of Differential Equations 1 Journal of Multivariate Analysis 1 Mathematics and Computers in Simulation 1 Quarterly of Applied Mathematics 1 Computer Aided Geometric Design 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Numerical Methods for Partial Differential Equations 1 Mathematical and Computer Modelling 1 SIAM Journal on Matrix Analysis and Applications 1 Journal of Scientific Computing 1 Applications of Mathematics 1 Numerical Algorithms 1 Bulletin of the American Mathematical Society. New Series 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Cybernetics and Systems Analysis 1 Computational Optimization and Applications 1 Communications in Numerical Methods in Engineering 1 Russian Journal of Mathematical Physics 1 Numerical Linear Algebra with Applications 1 Discrete and Continuous Dynamical Systems 1 Mathematical Problems in Engineering 1 Finance and Stochastics 1 Optimization Methods & Software 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Fractional Calculus & Applied Analysis 1 Sibirskiĭ Zhurnal Industrial’noĭ Matematiki 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Methodology and Computing in Applied Probability 1 The ANZIAM Journal 1 Computational Methods in Applied Mathematics 1 Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences 1 Central European Journal of Mathematics 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Optimization Letters 1 Advances in Numerical Analysis 1 Journal of Pseudo-Differential Operators and Applications 1 Analysis and Mathematical Physics
all top 5

#### Cited in 39 Fields

 168 Numerical analysis (65-XX) 78 Partial differential equations (35-XX) 56 Operator theory (47-XX) 34 Biology and other natural sciences (92-XX) 33 Integral transforms, operational calculus (44-XX) 28 Harmonic analysis on Euclidean spaces (42-XX) 25 Information and communication theory, circuits (94-XX) 16 Optics, electromagnetic theory (78-XX) 16 Geophysics (86-XX) 15 Integral equations (45-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 9 Functional analysis (46-XX) 9 Operations research, mathematical programming (90-XX) 7 Computer science (68-XX) 6 Approximations and expansions (41-XX) 6 Statistics (62-XX) 5 Functions of a complex variable (30-XX) 5 Mechanics of deformable solids (74-XX) 4 Ordinary differential equations (34-XX) 3 Probability theory and stochastic processes (60-XX) 3 Fluid mechanics (76-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Measure and integration (28-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Abstract harmonic analysis (43-XX) 2 Differential geometry (53-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Quantum theory (81-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) 1 Systems theory; control (93-XX)