## Inverse Problems

 Short Title: Inverse Probl. Publisher: IOP Publishing, Bristol ISSN: 0266-5611 Online: http://iopscience.iop.org/0266-5611 Comments: Indexed cover-to-cover
 Documents Indexed: 4,518 Publications (since 1985) References Indexed: 917 Publications with 35,522 References.
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### Authors

 73 Yamamoto, Masahiro 42 Klibanov, Michael V. 40 Ikehata, Masaru 36 Bertero, Mario 35 Somersalo, Erkki 33 Ramlau, Ronny 31 Borcea, Liliana 31 Burger, Martin 31 Colton, David Lem 31 Scherzer, Otmar 30 Cakoni, Fioralba 30 Kaltenbacher, Barbara 29 Cheney, Margaret 28 Bal, Guillaume 28 Hofmann, Bernd 27 Haddar, Houssem 27 Kaipio, Jari P. 27 Nakamura, Gen 27 Papanicolaou, George C. 26 Aktosun, Tuncay 26 Kirsch, Andreas 26 Kress, Rainer 26 Ramm, Alexander G. 24 Arridge, Simon R. 24 Louis, Alfred Karl 24 Monk, Peter B. 24 Siltanen, Samuli 23 Li, Peijun 23 Uhlmann, Gunther Alberto 23 Zou, Jun 22 Jin, Bangti 22 Piana, Michele 21 Hu, Guanghui 21 Rundell, William 20 Calvetti, Daniela 20 Hohage, Thorsten 20 Isakov, Victor M. 20 Lesselier, Dominique 20 Seo, Jin Keun 19 Fokas, Athanassios S. 19 Jin, Qinian 19 Lassas, Matti J. 19 Liu, Hongyu 19 Novikov, Roman G. 19 Schuster, Thomas 18 Boccacci, Patrizia 18 de Hoop, Maarten V. 18 Garnier, Josselin 18 Haltmeier, Markus 18 Liu, Xiaodong 18 Zhang, Bo 17 Bao, Gang 17 Boiti, Marco 17 Cheng, Jin 17 Haber, Eldad 17 Hyvönen, Nuutti 17 Kunyansky, Leonid A. 17 Pempinelli, Flora 17 Pike, E. R. 17 Potthast, Roland W. E. 16 El Badia, Abdellatif 16 Lionheart, William Robert Breckon 15 Defrise, Michel 15 McLaughlin, Joyce Rogers 15 Sabatier, Pierre C. 15 Tsogka, Chrysoula 14 Đinh Nho Hào 14 Dorn, Oliver 14 Grünbaum, Francisco Alberto 14 Han, Bo 14 Kang, Hyeonbae 14 Leitão, Antonio 14 Maass, Peter 14 Schönlieb, Carola-Bibiane 14 Shen, Chao-Liang 14 Sun, Jiguang 14 Symes, William W. 14 Yagle, Andrew E. 13 Akduman, Ibrahim 13 Engl, Heinz W. 13 Harrach, Bastian 13 Imanuvilov, Oleg Yu. 13 Kolehmainen, Ville 13 Lechleiter, Armin 13 Pereverzev, Sergei V. 13 Schotland, John C. 13 Stefanov, Plamen D. 13 Stuart, Andrew M. 13 van den Berg, Peter M. 12 Abubakar, Aria 12 Bellassoued, Mourad 12 Borden, Brett 12 Hasanoǧlu, Alemdar 12 Herman, Gabor T. 12 Hettlich, Frank 12 Mathé, Peter 12 Palamodov, Victor Pavlovitch 12 Rieder, Andreas 12 Sini, Mourad 12 Tautenhahn, Ulrich ...and 4,625 more Authors
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### Fields

 2,435 Partial differential equations (35-XX) 1,808 Numerical analysis (65-XX) 846 Optics, electromagnetic theory (78-XX) 577 Biology and other natural sciences (92-XX) 364 Information and communication theory, circuits (94-XX) 354 Operator theory (47-XX) 327 Integral transforms, operational calculus (44-XX) 295 Statistics (62-XX) 266 Geophysics (86-XX) 265 Fluid mechanics (76-XX) 264 Ordinary differential equations (34-XX) 260 Mechanics of deformable solids (74-XX) 231 Integral equations (45-XX) 199 Dynamical systems and ergodic theory (37-XX) 186 Calculus of variations and optimal control; optimization (49-XX) 157 Operations research, mathematical programming (90-XX) 145 Computer science (68-XX) 138 Quantum theory (81-XX) 91 Probability theory and stochastic processes (60-XX) 82 Harmonic analysis on Euclidean spaces (42-XX) 80 Systems theory; control (93-XX) 69 Global analysis, analysis on manifolds (58-XX) 54 Linear and multilinear algebra; matrix theory (15-XX) 48 Differential geometry (53-XX) 48 Statistical mechanics, structure of matter (82-XX) 43 Classical thermodynamics, heat transfer (80-XX) 40 Astronomy and astrophysics (85-XX) 37 Potential theory (31-XX) 33 Mechanics of particles and systems (70-XX) 30 Functional analysis (46-XX) 28 Functions of a complex variable (30-XX) 24 Difference and functional equations (39-XX) 22 Special functions (33-XX) 21 General and overarching topics; collections (00-XX) 19 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Approximations and expansions (41-XX) 12 Real functions (26-XX) 11 Relativity and gravitational theory (83-XX) 10 Abstract harmonic analysis (43-XX) 8 Combinatorics (05-XX) 6 Algebraic topology (55-XX) 4 History and biography (01-XX) 4 Topological groups, Lie groups (22-XX) 4 Sequences, series, summability (40-XX) 4 Convex and discrete geometry (52-XX) 3 Measure and integration (28-XX) 3 General topology (54-XX) 2 Nonassociative rings and algebras (17-XX) 2 Geometry (51-XX) 1 Number theory (11-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Manifolds and cell complexes (57-XX)

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3,644 Publications have been cited 41,729 times in 15,905 Documents Cited by Year
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Iterative oblique projection onto convex sets and the split feasibility problem. Zbl 0996.65048
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The multiple-sets split feasibility problem and its applications for inverse problems. Zbl 1089.65046
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A variable Krasnosel’skiĭ–Mann algorithm and the multiple-set split feasibility problem. Zbl 1126.47057
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Optical tomography in medical imaging. Zbl 0926.35155
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The relaxed CQ algorithm solving the split feasibility problem. Zbl 1066.65047
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Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces. Zbl 1213.65085
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Inverse scattering transform for the Camassa–Holm equation. Zbl 1105.37044
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Convergence rates for Tikhonov regularisation of nonlinear ill-posed problems. Zbl 0695.65037
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A simple method for solving inverse scattering problems in the resonance region. Zbl 0859.35133
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A note on the $$CQ$$ algorithm for the split feasibility problem. Zbl 1080.65033
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The split common fixed-point problem for demicontractive mappings. Zbl 1219.90185
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Solving the split feasibility problem without prior knowledge of matrix norms. Zbl 1262.90193
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Inverse problems and Carleman estimates. Zbl 0755.35151
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Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation. Zbl 1181.35322
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Multi-peakon solutions of the Degasperis-Procesi equation. Zbl 1041.35090
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2003
Electrical impedance tomography and Calderón’s problem. Zbl 1181.35339
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A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators. Zbl 1131.65046
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A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems. Zbl 0873.65057
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The stability for the Cauchy problem for elliptic equations. Zbl 1190.35228
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Multi-peakons and a theorem of Stieltjes. Zbl 0923.35154
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Electrical impedance tomography. Zbl 1031.35147
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Geometry of linear ill-posed problems in variable Hilbert spaces. Zbl 1026.65040
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Characterization of the shape of a scattering obstacle using the spectral data of the far field operator. Zbl 0919.35147
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1998
Carleman estimates for parabolic equations and applications. Zbl 1194.35512
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2009
A tutorial on inverse problems for anomalous diffusion processes. Zbl 1323.34027
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2015
Several solution methods for the split feasibility problem. Zbl 1080.65035
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2005
Lipschitz stability in inverse parabolic problems by the Carleman estimate. Zbl 0992.35110
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1998
Inverse problems in elasticity. Zbl 1070.35118
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Convergence rates of convex variational regularization. Zbl 1068.65085
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Sparsity and incoherence in compressive sampling. Zbl 1120.94005
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Structural identification of an unknown source term in a heat equation. Zbl 0917.35156
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Exponential instability in an inverse problem for the Schrödinger equation. Zbl 0985.35110
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2001
Tensor completion and low-$$n$$-rank tensor recovery via convex optimization. Zbl 1211.15036
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2011
Restricted isometry properties and nonconvex compressive sensing. Zbl 1143.94004
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Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction. Zbl 0916.35132
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Inverse source problem for a fractional diffusion equation. Zbl 1211.35280
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Global Lipschitz stability in an inverse hyperbolic problem by interior observations. Zbl 0983.35151
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2001
The strong convergence of a KM-CQ-like algorithm for a split feasibility problem. Zbl 1211.65065
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2011
Separable nonlinear least squares: The variable projection method and its applications. Zbl 1022.65014
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2003
Prolate spheroidal wavefunctions, quadrature and interpolation. Zbl 0991.65024
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2001
Thermoacoustic tomography with variable sound speed. Zbl 1177.35256
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2009
Analysis versus synthesis in signal priors. Zbl 1138.93055
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2007
The domain derivative and two applications in inverse scattering theory. Zbl 0773.35085
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Krasnoselski–Mann iteration for hierarchical fixed-point problems. Zbl 1128.47060
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2007
Proximity algorithms for image models: denoising. Zbl 1216.94015
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Boundary control in reconstruction of manifolds and metrics (the BC method). Zbl 0990.35135
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1997
A survey on sampling and probe methods for inverse problems. Zbl 1094.35144
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2006
An inverse problem for a one-dimensional time-fractional diffusion problem. Zbl 1247.35203
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2012
Solutions of inverse nodal problems. Zbl 0667.34020
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1989
Uniqueness and stability in an inverse problem for the Schrödinger equation. Zbl 1023.35091
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2002
Edge-preserving and scale-dependent properties of total variation regularization. Zbl 1043.94512
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2003
Level set methods for inverse scattering. Zbl 1191.35272
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2006
A finite-difference solution to an inverse problem for determining a control function in a parabolic partial differential equation. Zbl 0683.65106
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1989
Stability, reconstruction formula and regularization for an inverse source hyperbolic problem by a control method. Zbl 0822.35154
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1995
On the spectral transform of a Korteweg-de Vries equation in two spatial dimensions. Zbl 0617.35119
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An inverse problem in corrosion detection. Zbl 0882.35133
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1997
Simultaneous reconstruction of the initial temperature and heat radiative coefficient. Zbl 0987.35166
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2001
One new strategy for a priori choice of regularizing parameters in Tikhonov’s regularization. Zbl 0957.65052
Cheng, J.; Yamamoto, M.
2000
Level-set function approach to an inverse interface problem. Zbl 0986.35130
Ito, Kazufumi; Kunisch, Karl; Li, Zhilin
2001
Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography. Zbl 1044.78513
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2000
Logarithmic convergence rates of the iteratively regularized Gauss-Newton method for an inverse potential and an inverse scattering problem. Zbl 0895.35109
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1997
A simple method using Morozov’s discrepancy principle for solving inverse scattering problems. Zbl 0902.35123
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1997
Nonlinear integral equations and the iterative solution for an inverse boundary value problem. Zbl 1086.35139
Kress, Rainer; Rundell, William
2005
Solving Cauchy problems by minimizing an energy-like functional. Zbl 1089.35084
Andrieux, S.; Baranger, T. N.; Ben Abda, A.
2006
Uniqueness, stability and numerical methods for the inverse problem that arises in financial markets. Zbl 0938.35190
Bouchouev, Ilia; Isakov, Victor
1999
Ensemble Kalman methods for inverse problems. Zbl 1311.65064
Iglesias, Marco A.; Law, Kody J. H.; Stuart, Andrew M.
2013
Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates. Zbl 1205.65194
Egger, Herbert; Engl, Heinz W.
2005
Recent progress in the boundary control method. Zbl 1126.35089
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2007
Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation. Zbl 1281.65125
Li, Gongsheng; Zhang, Dali; Jia, Xianzheng; Yamamoto, Masahiro
2013
Optical tomography: forward and inverse problems. Zbl 1188.35197
Arridge, Simon R.; Schotland, John C.
2009
Linear spectral problems, nonlinear equations and the $${\bar \partial}$$- method. Zbl 0685.35080
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1989
Numerical procedures for the determination of an unknown coefficient in semi-linear parabolic differential equations. Zbl 0805.65133
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1994
Nonparametric statistical inverse problems. Zbl 1137.62323
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2008
Generalized KM theorems and their applications. Zbl 1117.65081
Yang, Qingzhi; Zhao, Jinling
2006
A scaled gradient projection method for constrained image deblurring. Zbl 1155.94011
Bonettini, S.; Zanella, R.; Zanni, L.
2009
Inverse spectral problems for Sturm-Liouville operators on graphs. Zbl 1089.34009
Yurko, V.
2005
Explicit inversion formulae for the spherical mean Radon transform. Zbl 1127.44003
Kunyansky, Leonid A.
2007
Inverse nodal problems for Sturm-Liouville equations with eigenparameter dependent boundary conditions. Zbl 0860.34007
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1996
Nonlinear evolution equations, rescalings, model PDEs and their integrability. I. Zbl 0645.35087
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1987
An inverse source problem in potential analysis. Zbl 0963.35194
2000
Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media. Zbl 1180.35563
Hristova, Yulia; Kuchment, Peter; Nguyen, Linh
2008
An iterative regularization method for the solution of the split feasibility problem in Banach spaces. Zbl 1153.46308
Schöpfer, F.; Schuster, T.; Louis, A. K.
2008
Cloaking via change of variables in electric impedance tomography. Zbl 1153.35406
Kohn, R. V.; Shen, H.; Vogelius, M. S.; Weinstein, M. I.
2008
Inverse scattering problems with multi-frequencies. Zbl 1332.78019
Bao, Gang; Li, Peijun; Lin, Junshan; Triki, Faouzi
2015
An implementation of the reconstruction algorithm of A. Nachman for the 2D inverse conductivity problem. Zbl 0962.35193
Siltanen, Samuli; Mueller, Jennifer; Isaacson, David
2000
Fréchet differentiability of boundary integral operators in inverse acoustic scattering. Zbl 0805.35157
Potthast, Roland
1994
Multisoliton solutions of the Degasperis-Procesi equation and their peakon limit. Zbl 1086.35095
Matsuno, Yoshimasa
2005
Numerical identification of parameters in parabolic systems. Zbl 0894.35127
Keung, Yee Lo; Zou, Jun
1998
Identification of Robin coefficients by the means of boundary measurements. Zbl 0943.35100
Chaabane, Slim; Jaoua, Mohamed
1999
MAP estimators and their consistency in Bayesian nonparametric inverse problems. Zbl 1281.62089
Dashti, M.; Law, K. J. H.; Stuart, A. M.; Voss, J.
2013
On the method of Lavrentiev regularization for nonlinear ill-posed problems. Zbl 1005.65058
Tautenhahn, U.
2002
Analytical and computational methods for transmission eigenvalues. Zbl 1192.78024
Colton, David; Monk, Peter; Sun, Jiguang
2010
On a global estimate in a linear inverse hyperbolic problem. Zbl 0862.35141
Puel, Jean-Pierre; Yamamoto, Masahiro
1996
Fréchet derivatives in inverse obstacle scattering. Zbl 0821.35147
Hettlich, Frank
1995
Uniqueness in inverse obstacle scattering. Zbl 0787.35119
Kirsch, Andreas; Kress, Rainer
1993
The MUSIC algorithm and the factorization method in inverse scattering theory for inhomogeneous media. Zbl 1027.35158
Kirsch, Andreas
2002
Prolongation algebras and Hamiltonian operators for peakon equations. Zbl 1020.35096
Hone, Andrew N. W.; Wang, Jing Ping
2003
Recovery of coefficients for a weighted $$p$$-Laplacian perturbed by a linear second order term. Zbl 1460.35386
Cârstea, Cătălin I.; Kar, Manas
2021
On Calderón’s inverse inclusion problem with smooth shapes by a single partial boundary measurement. Zbl 1467.35355
Liu, Hongyu; Tsou, Chun-Hsiang; Yang, Wei
2021
Recovering a quasilinear conductivity from boundary measurements. Zbl 1457.65172
Shankar, Ravi
2021
A projected Bouligand-Landweber iteration for non-smooth ill-posed problems. Zbl 07323231
Fu, Zhenwu; Chen, Yong; Han, Bo
2021
Unique continuation from a generalized impedance edge-corner for Maxwell’s system and applications to inverse problems. Zbl 1456.35192
Diao, Huaian; Liu, Hongyu; Zhang, Long; Zou, Jun
2021
Some inverse problems for wave equations with fractional derivative attenuation. Zbl 1459.35396
Kaltenbacher, Barbara; Rundell, William
2021
Monotonicity principle in tomography of nonlinear conducting materials. Zbl 1462.78012
Corbo Esposito, Antonio; Faella, Luisa; Piscitelli, Gianpaolo; Prakash, Ravi; Tamburrino, Antonello
2021
On a local geometric property of the generalized elastic transmission eigenfunctions and application. Zbl 1479.35286
Diao, Huaian; Liu, Hongyu; Sun, Baiyi
2021
Laboratory application of sampling approaches to inverse scattering. Zbl 1466.62451
2021
Adaptive regularisation for ensemble Kalman inversion. Zbl 1456.65095
Iglesias, Marco; Yang, Yuchen
2021
Shape reconstruction in linear elasticity: standard and linearized monotonicity method. Zbl 1461.74022
Eberle, Sarah; Harrach, Bastian
2021
Reconstruction of multipolar point sources with multi-frequency sparse far field data. Zbl 1466.35367
Ji, Xia
2021
A deterministic-statistical approach to reconstruct moving sources using sparse partial data. Zbl 1466.35369
Liu, Yanfang; Guo, Yukun; Sun, Jiguang
2021
Stabilizing invertible neural networks using mixture models. Zbl 07375643
Hagemann, Paul; Neumayer, Sebastian
2021
Oversmoothing Tikhonov regularization in Banach spaces. Zbl 1483.65086
Chen, De-Han; Hofmann, Bernd; Yousept, Irwin
2021
Projection methods for high numerical aperture phase retrieval. Zbl 1480.65142
Hieu Thao, Nguyen; Soloviev, Oleg; Luke, Russell; Verhaegen, Michel
2021
Phaseless inverse scattering with background information. Zbl 1473.35140
Novikov, R. G.; Sivkin, V. N.
2021
Stability estimates for the relativistic Schrödinger equation from partial boundary data. Zbl 1483.35344
Senapati, Soumen
2021
A direct method for solving inverse Sturm-Liouville problems. Zbl 07305940
Kravchenko, Vladislav V.; Torba, Sergii M.
2021
Unique determination for an inverse problem from the vortex dynamics. Zbl 1462.34041
Lai, Ru-Yu; Zhou, Hanming
2021
The interior inverse electromagnetic scattering for an inhomogeneous cavity. Zbl 1457.78012
Zeng, Fang; Meng, Shixu
2021
Non-stationary multi-layered Gaussian priors for Bayesian inversion. Zbl 1457.60097
Emzir, Muhammad; Lasanen, Sari; Purisha, Zenith; Roininen, Lassi; Särkkä, Simo
2021
Ultrasound modulated bioluminescence tomography with a single optical measurement. Zbl 1458.35420
Chung, Francis; Yang, Tianyu; Yang, Yang
2021
Deep synthesis network for regularizing inverse problems. Zbl 07310609
Obmann, Daniel; Schwab, Johannes; Haltmeier, Markus
2021
An inverse potential problem for subdiffusion: stability and reconstruction. Zbl 1458.35477
Jin, Bangti; Zhou, Zhi
2021
Tikhonov regularization for polynomial approximation problems in Gauss quadrature points. Zbl 1461.65010
An, Congpei; Wu, Hao-Ning
2021
The maximum entropy on the mean method for image deblurring. Zbl 07310613
Rioux, Gabriel; Choksi, Rustum; Hoheisel, Tim; Maréchal, Pierre; Scarvelis, Christopher
2021
Inverse initial boundary value problem for a non-linear hyperbolic partial differential equation. Zbl 1457.58016
Nakamura, Gen; Vashisth, Manmohan; Watanabe, Michiyuki
2021
Optimal experimental design for infinite-dimensional Bayesian inverse problems governed by PDEs: a review. Zbl 1461.62129
Alexanderian, Alen
2021
Sparsity-based nonlinear reconstruction of optical parameters in two-photon photoacoustic computed tomography. Zbl 1460.78011
Gupta, Madhu; Kumar Mishra, Rohit; Roy, Souvik
2021
Numerical solution of an inverse random source problem for the time fractional diffusion equation via PhaseLift. Zbl 1475.35432
Gong, Yuxuan; Li, Peijun; Wang, Xu; Xu, Xiang
2021
A range-relaxed criteria for choosing the Lagrange multipliers in the iterated Tikhonov Kaczmarz method for solving systems of linear ill-posed equations. Zbl 07323241
Filippozzi, R.; Rabelo, J. C.; Boiger, R.; Leitão, A.
2021
Regularisation, optimisation, subregularity. Zbl 07335387
Valkonen, T.
2021
Simultaneous inversion of the potential term and the fractional orders in a multi-term time-fractional diffusion equation. Zbl 1462.35469
Sun, L. L.; Li, Y. S.; Zhang, Y.
2021
Reconstruction of sources from time domain scattered waves at sparse sensors. Zbl 1467.35351
Ji, Xia
2021
Optimal-order convergence of Nesterov acceleration for linear ill-posed problems. Zbl 07357681
Kindermann, Stefan
2021
A new interpretation of (Tikhonov) regularization. Zbl 07357684
Gerth, Daniel
2021
3D Compton scattering imaging with multiple scattering: analysis by FIO and contour reconstruction. Zbl 1466.35372
Rigaud, Gaël
2021
Lippmann-Schwinger-Lanczos algorithm for inverse scattering problems. Zbl 07362502
Druskin, V.; Moskow, S.; Zaslavsky, M.
2021
Structure analysis of direct sampling method in 3D electromagnetic inverse problem: near- and far-field configuration. Zbl 07362505
Kang, Sangwoo; Lambert, Marc
2021
Unique recovery of unknown spatial load in damped Euler-Bernoulli beam equation from final time measured output. Zbl 1467.74036
Hasanov, Alemdar; Romanov, Vladimir; Baysal, Onur
2021
A projective two-point gradient Kaczmarz iteration for nonlinear ill-posed problems. Zbl 07362507
Gao, Guangyu; Han, Bo; Tong, Shanshan
2021
Inverse problems for nonlinear quasi-hemivariational inequalities with application to mixed boundary value problems. Zbl 1433.35462
Migórski, Stanisław; Khan, Akhtar A.; Zeng, Shengda
2020
NETT: solving inverse problems with deep neural networks. Zbl 1456.65038
Li, Housen; Schwab, Johannes; Antholzer, Stephan; Haltmeier, Markus
2020
Recovering piecewise constant refractive indices by a single far-field pattern. Zbl 1446.35262
Blåsten, Emilia; Liu, Hongyu
2020
The sliding Frank-Wolfe algorithm and its application to super-resolution microscopy. Zbl 1434.65082
Denoyelle, Quentin; Duval, Vincent; Peyré, Gabriel; Soubies, Emmanuel
2020
Convexification and experimental data for a 3D inverse scattering problem with the moving point source. Zbl 1446.35265
Khoa, Vo Anh; Bidney, Grant W.; Klibanov, Michael V.; Nguyen, Loc H.; Nguyen, Lam H.; Sullivan, Anders J.; Astratov, Vasily N.
2020
Stable determination of polygonal inclusions in Calderón’s problem by a single partial boundary measurement. Zbl 1445.35334
Liu, Hongyu; Tsou, Chun-Hsiang
2020
Convergence analysis of (statistical) inverse problems under conditional stability estimates. Zbl 07153871
Werner, Frank; Hofmann, Bernd
2020
Uniqueness in inverse cavity scattering problems with phaseless near-field data. Zbl 1460.35246
Zhang, Deyue; Wang, Yinglin; Guo, Yukun; Li, Jingzhi
2020
The inverse problem of reconstructing reaction-diffusion systems. Zbl 1444.65055
Kaltenbacher, Barbara; Rundell, William
2020
Fast acoustic source imaging using multi-frequency sparse data. Zbl 1448.35566
Alzaalig, Ala; Hu, Guanghui; Liu, Xiaodong; Sun, Jiguang
2020
Half-inverse Sturm-Liouville problem on a time scale. Zbl 1433.93084
2020
An inverse acoustic-elastic interaction problem with phased or phaseless far-field data. Zbl 1437.35702
Dong, Heping; Lai, Jun; Li, Peijun
2020
Convergence rates of Tikhonov regularizations for elliptic and parabolic inverse radiativity problems. Zbl 07220290
Chen, De-Han; Jiang, Daijun; Zou, Jun
2020
Stability for inverse source problems by Carleman estimates. Zbl 1459.35393
Huang, X.; Yu Imanuvilov, Oleg; Yamamoto, M.
2020
Sparse reconstructions from few noisy data: analysis of hierarchical Bayesian models with generalized gamma hyperpriors. Zbl 1464.62365
Calvetti, Daniela; Pragliola, Monica; Somersalo, Erkki; Strang, Alexander
2020
Unique reconstruction of the potential for the interior transmission eigenvalue problem for spherically stratified media. Zbl 1436.35328
Wei, Zhaoying; Wei, Guangsheng
2020
The Calderón problem for the fractional magnetic operator. Zbl 1443.35194
Li, Li
2020
Optimal experimental design under irreducible uncertainty for linear inverse problems governed by PDEs. Zbl 1443.62213
Koval, Karina; Alexanderian, Alen; Stadler, Georg
2020
Numerical schemes to reconstruct three-dimensional time-dependent point sources of acoustic waves. Zbl 1471.65122
Chen, Bo; Guo, Yukun; Ma, Fuming; Sun, Yao
2020
Consistency of Bayesian inference with Gaussian process priors in an elliptic inverse problem. Zbl 1445.35330
Giordano, Matteo; Nickl, Richard
2020
On a regularization approach to the inverse transmission eigenvalue problem. Zbl 1454.34036
Buterin, S. A.; Choque-Rivero, A. E.; Kuznetsova, M. A.
2020
$$\ell_1-\alpha\ell_2$$ minimization methods for signal and image reconstruction with impulsive noise removal. Zbl 1468.94021
Li, Peng; Chen, Wengu; Ge, Huanmin; Ng, Michael K.
2020
Preconditioning inverse problems for hyperbolic equations with applications to photoacoustic tomography. Zbl 07153865
Beigl, Alexander; Scherzer, Otmar; Sogn, Jarle; Zulehner, Walter
2020
A new temporal control approach for SCAO systems. Zbl 1440.93131
Pöttinger, Markus; Ramlau, Ronny; Auzinger, Günter
2020
Compton scattering tomography in translational geometries. Zbl 1466.44002
Webber, James; Miller, Eric L.
2020
Persistent homology detects curvature. Zbl 07161824
Bubenik, Peter; Hull, Michael; Patel, Dhruv; Whittle, Benjamin
2020
Inverse transport problem in fluorescence ultrasound modulated optical tomography with angularly averaged measurements. Zbl 1466.35370
Li, Wei; Yang, Yang; Zhong, Yimin
2020
Recovery of singularities for the weighted cone transform appearing in Compton camera imaging. Zbl 1442.44003
Zhang, Yang
2020
Analysis of shape optimization problems for unsteady fluid-structure interaction. Zbl 1440.49044
Haubner, Johannes; Ulbrich, Michael; Ulbrich, Stefan
2020
Deep unfolding of a proximal interior point method for image restoration. Zbl 1452.94003
Bertocchi, Carla; Chouzenoux, Emilie; Corbineau, Marie-Caroline; Pesquet, Jean-Christophe; Prato, Marco
2020
Modulus-based iterative methods for constrained $$\ell_p$$-$$\ell_q$$ minimization. Zbl 1451.65072
Buccini, A.; Pasha, M.; Reichel, L.
2020
On the inverse spectral stability for the transmission eigenvalue problem with finite data. Zbl 1470.34054
Xu, Xiao-Chuan; Yang, Chuan-Fu
2020
Monotonicity in inverse obstacle scattering on unbounded domains. Zbl 1458.35469
Albicker, Annalena; Griesmaier, Roland
2020
Geometry of the phase retrieval problem. Zbl 1451.49037
Barnett, Alexander H.; Epstein, Charles L.; Greengard, Leslie F.; Magland, Jeremy F.
2020
An inverse problem for the fractional Schrödinger equation in a magnetic field. Zbl 1473.35500
Covi, Giovanni
2020
The quadratic Wasserstein metric for inverse data matching. Zbl 1465.49029
Engquist, Björn; Ren, Kui; Yang, Yunan
2020
A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium. Zbl 1433.78016
Fujiwara, Hiroshi; Sadiq, Kamran; Tamasan, Alexandru
2020
Image reconstruction through metamorphosis. Zbl 1447.94005
Gris, Barbara; Chen, Chong; Öktem, Ozan
2020
Determining both the source of a wave and its speed in a medium from boundary measurements. Zbl 1458.35480
2020
A Nash game based variational model for joint image intensity correction and registration to deal with varying illumination. Zbl 1452.94009
Theljani, Anis; Chen, Ke
2020
The fixed angle scattering problem and wave equation inverse problems with two measurements. Zbl 1439.35569
Rakesh; Salo, Mikko
2020
Applications of kinetic tools to inverse transport problems. Zbl 1452.65211
Li, Qin; Sun, Weiran
2020
The bound-state soliton solutions of the complex modified KdV equation. Zbl 1447.35290
Zhang, Yongshuai; Tao, Xiangxing; Xu, Shuwei
2020
Bayesian approach to inverse time-harmonic acoustic scattering with phaseless far-field data. Zbl 1443.76205
Yang, Zhipeng; Gui, Xinping; Ming, Ju; Hu, Guanghui
2020
Mathematical modeling for 2D light-sheet fluorescence microscopy image reconstruction. Zbl 1444.65062
Cueva, Evelyn; Courdurier, Matias; Osses, Axel; Castañeda, Victor; Palacios, Benjamin; Härtel, Steffen
2020
Semiclassical inverse spectral problem for seismic surface waves in isotropic media. I: Love waves. Zbl 1442.86003
de Hoop, Maarten V.; Iantchenko, Alexei; van der Hilst, Robert D.; Zhai, Jian
2020
Analysis of a heuristic rule for the IRGNM in Banach spaces with convex regularization terms. Zbl 1445.49018
Fu, Zhenwu; Jin, Qinian; Zhang, Zhengqiang; Han, Bo; Chen, Yong
2020
Convexification for an inverse parabolic problem. Zbl 1445.35333
Klibanov, Michael V.; Li, Jingzhi; Zhang, Wenlong
2020
Numerical solution of inverse problems by weak adversarial networks. Zbl 1452.65308
Bao, Gang; Ye, Xiaojing; Zang, Yaohua; Zhou, Haomin
2020
Hölder-logarithmic stability in Fourier synthesis. Zbl 1453.42008
Isaev, Mikhail; Novikov, Roman G.
2020
Deep neural network expression of posterior expectations in Bayesian PDE inversion. Zbl 1453.35191
Herrmann, Lukas; Schwab, Christoph; Zech, Jakob
2020
Geometric numerical integration of the assignment flow. Zbl 07371339
Zeilmann, Alexander; Savarino, Fabrizio; Petra, Stefania; Schnörr, Christoph
2020
An inverse random source problem in a stochastic fractional diffusion equation. Zbl 1469.35259
Niu, Pingping; Helin, Tapio; Zhang, Zhidong
2020
An inverse random source problem for the time fractional diffusion equation driven by a fractional Brownian motion. Zbl 1469.35251
Feng, Xiaoli; Li, Peijun; Wang, Xu
2020
An image sharpening operator combined with framelet for image deblurring. Zbl 1468.94022
Liu, Jingjing; Lou, Yifei; Ni, Guoxi; Zeng, Tieyong
2020
Bilevel optimization, deep learning and fractional Laplacian regularization with applications in tomography. Zbl 07371382
Antil, Harbir; Di, Zichao Wendy; Khatri, Ratna
2020
Quasi-best approximation in optimization with PDE constraints. Zbl 1457.49022
Gaspoz, Fernando; Kreuzer, Christian; Veeser, Andreas; Wollner, Winnifried
2020
Reconstruction of the principal coefficient in the damped wave equation from Dirichlet-to-Neumann operator. Zbl 1457.35094
2020
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### Cited by 14,800 Authors

 135 Yamamoto, Masahiro 81 Uhlmann, Gunther Alberto 78 Fu, Chuli 77 Klibanov, Michael V. 76 Nguyen Huy Tuan 74 Ammari, Habib M. 74 Lesnic, Daniel 71 Yang, Chuanfu 62 Yurko, Vjacheslav Anatoljevich 60 Scherzer, Otmar 59 Liu, Hongyu 58 Dehghan Takht Fooladi, Mehdi 58 Hofmann, Bernd 58 Ma, Wen-Xiu 56 Lassas, Matti J. 55 Yao, Jen-Chih 55 Yao, Yonghong 53 Liu, Jijun 52 Ramm, Alexander G. 52 Xiong, Xiangtuan 52 Yin, Zhaoyang 51 Wei, Ting 50 Kaltenbacher, Barbara 49 Ceng, Lu-Chuan 47 Hu, Guanghui 46 Li, Peijun 46 Zou, Jun 45 Liou, Yeongcheng 45 Shehu, Yekini 44 Nakamura, Gen 43 Banks, Harvey Thomas 43 de Hoop, Maarten V. 43 Han, Bo 43 Jin, Bangti 42 Fan, Engui 41 Bellassoued, Mourad 41 Geng, Xianguo 40 Cakoni, Fioralba 38 Garnier, Josselin 38 Haddar, Houssem 38 Hasanoǧlu, Alemdar 37 Bao, Gang 37 Bondarenko, Natalia P. 37 Fokas, Athanassios S. 37 Kian, Yavar 37 Kress, Rainer 37 Salo, Mikko 37 Stuart, Andrew M. 36 Bal, Guillaume 36 Marin, Liviu 36 Pereverzev, Sergei V. 36 Reichel, Lothar 36 Sakhnovich, Alexander L. 35 Lu, Shuai 35 Yang, Fan 34 Chang, Shih-Sen 34 Kumam, Poom 34 Liu, Chein-Shan 34 Oksanen, Lauri 34 Ramlau, Ronny 33 Burger, Martin 33 Kang, Hyeonbae 33 Mathé, Peter 33 Vessella, Sergio 32 Cheng, Jin 32 George, Santhosh 32 Haltmeier, Markus 32 Hon, Yiu-Chung 32 Van der Mee, Cornelis Victor Maria 32 Wen, Chingfeng 32 Yan, Guozheng 31 Choulli, Mourad 31 Huang, Ting-Zhu 31 Kunisch, Karl 31 Wei, Guangsheng 30 Hyvönen, Nuutti 30 Li, Jingzhi 30 Ma, Fuming 30 Novikov, Roman G. 30 Novotny, Antonio André 30 Park, Won-Kwang 30 Sini, Mourad 30 Stefanov, Plamen D. 29 Censor, Yair 29 Cholamjiak, Prasit 29 Korotyaev, Evgeny L. 29 Mewomo, Oluwatosin Temitope 29 Xu, Hong-Kun 28 Belishev, Mikhail Igorevitch 28 Harrach, Bastian 28 Jin, Qinian 28 Trong, Dang Duc 28 Wang, Jenn-Nan 27 Aktosun, Tuncay 27 Borcea, Liliana 27 Buterin, Sergey Alexandrovich 27 Cheng, Xiaoliang 27 Cho, Yeol Je 27 Colton, David Lem 27 Đinh Nho Hào ...and 14,700 more Authors
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### Cited in 769 Journals

 732 Inverse Problems 483 Inverse Problems in Science and Engineering 467 Journal of Mathematical Physics 413 Journal of Inverse and Ill-Posed Problems 410 Journal of Computational and Applied Mathematics 402 Applied Mathematics and Computation 356 Journal of Mathematical Analysis and Applications 351 Applicable Analysis 324 Inverse Problems and Imaging 303 Journal of Computational Physics 232 Computers & Mathematics with Applications 211 SIAM Journal on Imaging Sciences 199 Journal of Differential Equations 178 Numerical Algorithms 168 Applied Mathematics Letters 158 SIAM Journal on Scientific Computing 157 Mathematical Methods in the Applied Sciences 146 Computer Methods in Applied Mechanics and Engineering 144 Applied and Computational Harmonic Analysis 138 Journal of Nonlinear Mathematical Physics 135 Theoretical and Mathematical Physics 130 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 128 Journal of Scientific Computing 126 Numerical Functional Analysis and Optimization 125 Journal of Inequalities and Applications 124 SIAM Journal on Mathematical Analysis 123 Applied Numerical Mathematics 123 Linear Algebra and its Applications 120 SIAM Journal on Applied Mathematics 118 Abstract and Applied Analysis 114 Fixed Point Theory and Applications 110 Wave Motion 109 Mathematical Problems in Engineering 105 Journal of Mathematical Imaging and Vision 104 Applied Mathematical Modelling 102 Optimization 99 Journal of Optimization Theory and Applications 97 Communications in Mathematical Physics 97 Engineering Analysis with Boundary Elements 89 Numerische Mathematik 88 Communications in Partial Differential Equations 85 International Journal of Computer Mathematics 80 Computational Optimization and Applications 73 Journal of Functional Analysis 71 Physica D 68 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 67 Computational and Applied Mathematics 67 Boundary Value Problems 64 Advances in Computational Mathematics 64 SIAM/ASA Journal on Uncertainty Quantification 63 Journal of Integral Equations and Applications 62 Chaos, Solitons and Fractals 62 Communications in Nonlinear Science and Numerical Simulation 62 Computational Geosciences 61 Mathematics of Computation 60 Mathematics and Computers in Simulation 58 SIAM Journal on Numerical Analysis 58 Journal of Mathematical Sciences (New York) 56 Journal de Mathématiques Pures et Appliquées. Neuvième Série 56 Nonlinear Analysis. Real World Applications 56 Comptes Rendus. Mathématique. Académie des Sciences, Paris 55 Journal of Applied Mathematics 54 Physics Letters. A 54 The Journal of Fourier Analysis and Applications 53 Studies in Applied Mathematics 53 Analysis and Mathematical Physics 49 Journal of Geometry and Physics 48 Proceedings of the American Mathematical Society 48 Results in Mathematics 48 Transactions of the American Mathematical Society 48 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 47 The Annals of Statistics 46 Acta Applicandae Mathematicae 46 Advances in Difference Equations 45 Letters in Mathematical Physics 45 BIT 45 Mathematical and Computer Modelling 45 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 44 Journal of Nonlinear Science and Applications 43 Archive for Rational Mechanics and Analysis 42 Advances in Mathematical Physics 41 Applied Mathematics and Optimization 41 SIAM Journal on Optimization 40 Integral Equations and Operator Theory 40 Acta Mathematicae Applicatae Sinica. English Series 39 Discrete and Continuous Dynamical Systems 39 Differential Equations 39 Electronic Journal of Statistics 37 Mathematical Notes 37 Advances in Mathematics 37 Foundations of Computational Mathematics 36 International Journal for Numerical Methods in Engineering 36 Quarterly of Applied Mathematics 34 The Journal of Geometric Analysis 33 Computational Mechanics 33 GEM - International Journal on Geomathematics 32 Reports on Mathematical Physics 32 SIAM Journal on Control and Optimization 32 Mathematical Programming. Series A. Series B 32 Journal of Fixed Point Theory and Applications ...and 669 more Journals
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### Cited in 61 Fields

 6,830 Partial differential equations (35-XX) 5,911 Numerical analysis (65-XX) 2,020 Operator theory (47-XX) 1,343 Calculus of variations and optimal control; optimization (49-XX) 1,287 Dynamical systems and ergodic theory (37-XX) 1,266 Optics, electromagnetic theory (78-XX) 1,174 Information and communication theory, circuits (94-XX) 1,140 Operations research, mathematical programming (90-XX) 1,123 Ordinary differential equations (34-XX) 981 Statistics (62-XX) 967 Biology and other natural sciences (92-XX) 953 Mechanics of deformable solids (74-XX) 817 Fluid mechanics (76-XX) 803 Computer science (68-XX) 538 Integral equations (45-XX) 514 Quantum theory (81-XX) 479 Integral transforms, operational calculus (44-XX) 449 Systems theory; control (93-XX) 436 Linear and multilinear algebra; matrix theory (15-XX) 420 Geophysics (86-XX) 417 Harmonic analysis on Euclidean spaces (42-XX) 397 Probability theory and stochastic processes (60-XX) 280 Classical thermodynamics, heat transfer (80-XX) 278 Global analysis, analysis on manifolds (58-XX) 225 Differential geometry (53-XX) 211 Approximations and expansions (41-XX) 210 Functional analysis (46-XX) 195 Statistical mechanics, structure of matter (82-XX) 182 Special functions (33-XX) 145 Real functions (26-XX) 144 Difference and functional equations (39-XX) 141 Mechanics of particles and systems (70-XX) 140 Potential theory (31-XX) 139 Functions of a complex variable (30-XX) 129 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 69 Combinatorics (05-XX) 66 Nonassociative rings and algebras (17-XX) 65 Algebraic geometry (14-XX) 50 General topology (54-XX) 47 Convex and discrete geometry (52-XX) 45 Algebraic topology (55-XX) 45 Astronomy and astrophysics (85-XX) 43 Relativity and gravitational theory (83-XX) 42 Abstract harmonic analysis (43-XX) 31 General and overarching topics; collections (00-XX) 28 Measure and integration (28-XX) 24 Topological groups, Lie groups (22-XX) 21 Several complex variables and analytic spaces (32-XX) 20 Number theory (11-XX) 19 Associative rings and algebras (16-XX) 19 Manifolds and cell complexes (57-XX) 15 History and biography (01-XX) 11 Geometry (51-XX) 9 Commutative algebra (13-XX) 8 Mathematics education (97-XX) 6 Group theory and generalizations (20-XX) 6 Sequences, series, summability (40-XX) 5 Field theory and polynomials (12-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Category theory; homological algebra (18-XX) 1 Mathematical logic and foundations (03-XX)