## Foundations of Computational Mathematics

### The Journal of the Society for the Foundations of Computational Mathematics

 Short Title: Found. Comput. Math. Publisher: Springer US, New York, NY ISSN: 1615-3375; 1615-3383/e Online: http://link.springer.com/journal/volumesAndIssues/10208 Comments: Indexed cover-to-cover
 Documents Indexed: 611 Publications (since 2001) References Indexed: 495 Publications with 18,538 References.
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### Latest Issues

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### Authors

 10 Beltrán, Carlos 10 Shub, Michael 9 Bürgisser, Peter 9 Cucker, Felipe 8 Chartier, Philippe 8 Cohen, Albert 8 DeVore, Ronald A. 8 Iserles, Arieh 8 Mrozek, Marian 8 Murua, Ander 8 Smale, Steve 7 Munthe-Kaas, Hans Z. 7 Sturmfels, Bernd 6 Basu, Saugata 6 Mansfield, Elizabeth Louise 6 McLachlan, Robert I. 6 Pardo, Luis Miguel 6 Woźniakowski, Henryk 5 Armentano, Diego 5 Candès, Emmanuel J. 5 Cohen-Steiner, David 5 Dahmen, Wolfgang A. 5 Edelsbrunner, Herbert 5 Giusti, Marc 5 Grigor’ev, Dmitriĭ Yur’evich 5 Krick, Teresa 5 Lecerf, Grégoire 5 Lubich, Christian 5 Malajovich, Gregorio 5 Mischaikow, Konstantin 5 Müller-Gronbach, Thomas 5 Nochetto, Ricardo Horacio 5 Ritter, Klaus 5 Sanz-Serna, Jesús María 5 Schwab, Christoph 5 Zgliczyński, Piotr 4 Bachmayr, Markus 4 Caponnetto, Andrea 4 Demanet, Laurent 4 Drusvyatskiy, Dmitriy 4 Dyn, Nira 4 Edelman, Alan Stuart 4 Hairer, Ernst 4 Harer, John L. 4 Hauenstein, Jonathan D. 4 Hydon, Peter Ellsworth 4 Jentzen, Arnulf 4 Leok, Melvin 4 Mémoli, Facundo 4 Nie, Jiawang 4 Quispel, Gilles Reinout Willem 4 Saff, Edward Barry 4 Sottile, Frank 4 Stern, Ari 4 Temlyakov, Vladimir Nikolaevich 4 Yampolsky, Michael 3 Adcock, Ben 3 Baratchart, Laurent 3 Barvinok, Alexander I. 3 Chandrasekaran, Venkat 3 Charon, Nicolas 3 Davis, Damek 3 De Loera, Jesús A. 3 Dereich, Steffen 3 Ebrahimi-Fard, Kurusch 3 Freedman, Michael Hartley 3 Grohs, Philipp 3 Hauser, Raphael Andreas 3 Heintz, Joos 3 Holm, Darryl Dallas 3 Hubert, Evelyne 3 Huybrechs, Daan 3 Landi, Claudia 3 Landsberg, Joseph Montague 3 Leviatan, Dany 3 Lewis, Adrian S. 3 Lim, Lek-Heng 3 Lotz, Martin 3 Lundervold, Alexander 3 Marsden, Jerrold Eldon 3 Matera, Guillermo 3 Meer, Klaus 3 Mérigot, Quentin 3 Mishra, Siddhartha 3 Montanari, Andrea 3 Nanda, Vidit 3 Nesterov, Yurii 3 Olver, Peter John 3 Olver, Sheehan Shakiban 3 Oudot, Steve Yann 3 Peyré, Gabriel 3 Pilarczyk, Paweł 3 Ranestad, Kristian 3 Recht, Benjamin 3 Renegar, James 3 Romberg, Justin K. 3 Rosasco, Lorenzo A. 3 Salvy, Bruno 3 Stevenson, Rob P. 3 Strohmer, Thomas ...and 871 more Authors
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### Fields

 301 Numerical analysis (65-XX) 154 Computer science (68-XX) 94 Partial differential equations (35-XX) 78 Algebraic geometry (14-XX) 77 Operations research, mathematical programming (90-XX) 66 Approximations and expansions (41-XX) 62 Dynamical systems and ergodic theory (37-XX) 53 Linear and multilinear algebra; matrix theory (15-XX) 45 Probability theory and stochastic processes (60-XX) 41 Statistics (62-XX) 40 Algebraic topology (55-XX) 37 Ordinary differential equations (34-XX) 36 Commutative algebra (13-XX) 35 Calculus of variations and optimal control; optimization (49-XX) 34 Global analysis, analysis on manifolds (58-XX) 32 Convex and discrete geometry (52-XX) 32 Differential geometry (53-XX) 26 Harmonic analysis on Euclidean spaces (42-XX) 26 Operator theory (47-XX) 25 Functional analysis (46-XX) 23 Information and communication theory, circuits (94-XX) 22 Number theory (11-XX) 20 Manifolds and cell complexes (57-XX) 19 Field theory and polynomials (12-XX) 19 Mechanics of particles and systems (70-XX) 15 Combinatorics (05-XX) 14 Functions of a complex variable (30-XX) 13 Fluid mechanics (76-XX) 12 Associative rings and algebras (16-XX) 11 Nonassociative rings and algebras (17-XX) 10 Mathematical logic and foundations (03-XX) 9 Topological groups, Lie groups (22-XX) 9 Quantum theory (81-XX) 9 Systems theory; control (93-XX) 8 Category theory; homological algebra (18-XX) 8 Biology and other natural sciences (92-XX) 7 Several complex variables and analytic spaces (32-XX) 7 General topology (54-XX) 7 Statistical mechanics, structure of matter (82-XX) 6 Special functions (33-XX) 6 Geometry (51-XX) 5 Group theory and generalizations (20-XX) 5 Real functions (26-XX) 5 Difference and functional equations (39-XX) 5 Optics, electromagnetic theory (78-XX) 4 Mechanics of deformable solids (74-XX) 3 General and overarching topics; collections (00-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Measure and integration (28-XX) 3 Potential theory (31-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Integral transforms, operational calculus (44-XX) 1 History and biography (01-XX) 1 $$K$$-theory (19-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Classical thermodynamics, heat transfer (80-XX)

### Citations contained in zbMATH Open

572 Publications have been cited 9,570 times in 7,314 Documents Cited by Year
Exact matrix completion via convex optimization. Zbl 1219.90124
Candès, Emmanuel J.; Recht, Benjamin
2009
User-friendly tail bounds for sums of random matrices. Zbl 1259.60008
Tropp, Joel A.
2012
Optimality of a standard adaptive finite element method. Zbl 1136.65109
Stevenson, Rob
2007
Optimal rates for the regularized least-squares algorithm. Zbl 1129.68058
Caponnetto, A.; De Vito, E.
2007
Convergence rates of best $$N$$-term Galerkin approximations for a class of elliptic SPDEs. Zbl 1206.60064
Cohen, Albert; DeVore, Ronald; Schwab, Christoph
2010
The convex geometry of linear inverse problems. Zbl 1280.52008
Chandrasekaran, Venkat; Recht, Benjamin; Parrilo, Pablo A.; Willsky, Alan S.
2012
A rigorous ODE solver and Smale’s 14th problem. Zbl 1047.37012
Tucker, Warwick
2002
Learning rates of least-square regularized regression. Zbl 1100.68100
Wu, Qiang; Ying, Yiming; Zhou, Ding-Xuan
2006
A PDE approach to fractional diffusion in general domains: a priori error analysis. Zbl 1347.65178
Nochetto, Ricardo H.; Otárola, Enrique; Salgado, Abner J.
2015
O’Donoghue, Brendan; Candès, Emmanuel
2015
Adaptive wavelet methods. II: Beyond the elliptic case. Zbl 1025.65056
Cohen, A.; Dahmen, W.; DeVore, R.
2002
On the ranks and border ranks of symmetric tensors. Zbl 1196.15024
Landsberg, J. M.; Teitler, Zach
2010
Best choices for regularization parameters in learning theory: on the bias-variance problem. Zbl 1057.68085
Cucker, Felipe; Smale, Steve
2002
Nonlinear methods of approximation. Zbl 1039.41012
Temlyakov, V. N.
2003
Local linear convergence for alternating and averaged nonconvex projections. Zbl 1169.49030
Lewis, A. S.; Luke, D. R.; Malick, J.
2009
Trust-region methods on Riemannian manifolds. Zbl 1129.65045
Absil, P.-A.; Baker, C. G.; Gallivan, K. A.
2007
On the stability and accuracy of least squares approximations. Zbl 1276.93086
Cohen, Albert; Davenport, Mark A.; Leviatan, Dany
2013
The Euclidean distance degree of an algebraic variety. Zbl 1370.51020
Draisma, Jan; Horobeţ, Emil; Ottaviani, Giorgio; Sturmfels, Bernd; Thomas, Rekha R.
2016
High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs. Zbl 1298.65022
Chkifa, Abdellah; Cohen, Albert; Schwab, Christoph
2014
Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit. Zbl 1183.68739
Needell, Deanna; Vershynin, Roman
2009
On the rank of a binary form. Zbl 1211.14059
Comas, Gonzalo; Seiguer, Malena
2011
Model selection for regularized least-squares algorithm in learning theory. Zbl 1083.68106
Vito, E.; Caponnetto, A.; Rosasco, L.
2005
Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems. Zbl 1341.65029
Wang, Bin; Iserles, Arieh; Wu, Xinyuan
2016
Smooth and algebraic invariants of a group action: Local and global constructions. Zbl 1145.53006
Hubert, Evelyne; Kogan, Irina A.
2007
Zigzag persistence. Zbl 1204.68242
Carlsson, Gunnar; de Silva, Vin
2010
Random gradient-free minimization of convex functions. Zbl 1380.90220
2017
Hyperbolic programs, and their derivative relaxations. Zbl 1130.90363
Renegar, James
2006
On the ideals of secant varieties of Segre varieties. Zbl 1068.14068
Landsberg, J. M.; Manivel, L.
2004
Exact support recovery for sparse spikes deconvolution. Zbl 1327.65104
Duval, Vincent; Peyré, Gabriel
2015
On the Riemannian geometry defined by self-concordant barriers and interior-point methods. Zbl 1049.90127
Nesterov, Yu. E.; Todd, M. J.
2002
Quantitative robust uncertainty principles and optimally sparse decompositions. Zbl 1102.94020
Candès, Emmanuel J.; Romberg, Justin
2006
An interpolating distance between optimal transport and Fisher-Rao metrics. Zbl 1385.49031
Chizat, Lénaïc; Peyré, Gabriel; Schmitzer, Bernhard; Vialard, François-Xavier
2018
Solving quadratic equations via phaselift when there are about as many equations as unknowns. Zbl 1312.90054
Candès, Emmanuel J.; Li, Xiaodong
2014
Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry. Zbl 1382.92272
Müller, Stefan; Feliu, Elisenda; Regensburger, Georg; Conradi, Carsten; Shiu, Anne; Dickenstein, Alicia
2016
Symmetric exponential integrators with an application to the cubic Schrödinger equation. Zbl 1147.65102
Celledoni, Elena; Cohen, David; Owren, Brynjulf
2008
Calculus of the exponent of Kurdyka-Łojasiewicz inequality and its applications to linear convergence of first-order methods. Zbl 1405.90076
Li, Guoyin; Pong, Ting Kei
2018
The theory of the interleaving distance on multidimensional persistence modules. Zbl 1335.55006
Lesnick, Michael
2015
The serendipity family of finite elements. Zbl 1218.65125
Arnold, Douglas N.; Awanou, Gerard
2011
A geometric analysis of phase retrieval. Zbl 1401.94049
Sun, Ju; Qu, Qing; Wright, John
2018
Geometric inference for probability measures. Zbl 1230.62074
Chazal, Frédéric; Cohen-Steiner, David; Mérigot, Quentin
2011
Hamilton-Pontryagin integrators on Lie groups. I: Introduction and structure-preserving properties. Zbl 1221.37166
Bou-Rabee, Nawaf; Marsden, Jerrold E.
2009
Metamorphoses through Lie group action. Zbl 1099.68116
Trouvé, Alain; Younes, Laurent
2005
Exponentials reproducing subdivision schemes. Zbl 1095.41001
Dyn, Nira; Levin, David; Luzzatto, Ariel
2003
Exact computation of joint spectral characteristics of linear operators. Zbl 1273.65054
2013
Analysis of a new nonlinear subdivision scheme. Applications in image processing. Zbl 1106.41001
Amat, Sergio; Donat, Rosa; Liandrat, Jacques; Trillo, J. Carlos
2006
Infinite-dimensional quadrature and approximation of distributions. Zbl 1177.65011
Creutzig, Jakob; Dereich, Steffen; Müller-Gronbach, Thomas; Ritter, Klaus
2009
Transversality and alternating projections for nonconvex sets. Zbl 1338.49057
Drusvyatskiy, D.; Ioffe, A. D.; Lewis, A. S.
2015
Multi-level quasi-Monte Carlo finite element methods for a class of elliptic PDEs with random coefficients. Zbl 1318.65006
Kuo, Frances Y.; Schwab, Christoph; Sloan, Ian H.
2015
The $$\mathcal A$$-truncated $$K$$-moment problem. Zbl 1331.65172
Nie, Jiawang
2014
Analysis of discrete $$L^2$$ projection on polynomial spaces with random evaluations. Zbl 1301.41005
Migliorati, G.; Nobile, F.; von Schwerin, E.; Tempone, R.
2014
A theoretical and computational framework for isometry invariant recognition of point cloud data. Zbl 1101.53022
Mémoli, Facundo; Sapiro, Guillermo
2005
On tensor completion via nuclear norm minimization. Zbl 1378.90066
Yuan, Ming; Zhang, Cun-Hui
2016
Construction of approximate entropy measure-valued solutions for hyperbolic systems of conservation laws. Zbl 1371.65080
Fjordholm, Ulrik S.; Käppeli, Roger; Mishra, Siddhartha; Tadmor, Eitan
2017
A unifying local convergence result for Newton’s method in Riemannian manifolds. Zbl 1147.58008
Alvarez, F.; Bolte, J.; Munier, J.
2008
$$C^1$$ Lohner algorithm. Zbl 1049.65038
Zgliczynski, Piotr
2002
Rigorous numerics for partial differential equations: The Kuramoto-Sivashinsky equation. Zbl 0984.65101
Zgliczyński, Piotr; Mischaikow, Konstantin
2001
Lipschitz functions have $$L_{p}$$-stable persistence. Zbl 1192.55007
Cohen-Steiner, David; Edelsbrunner, Herbert; Harer, John; Mileyko, Yuriy
2010
An algorithmic approach to chain recurrence. Zbl 1099.37010
Kalies, W. D.; Mischaikow, K.; VanderVorst, R. C. A. M.
2005
Algebraic structures of B-series. Zbl 1201.65124
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
2010
Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations. Zbl 1357.65153
Bachmayr, Markus; Schneider, Reinhold; Uschmajew, André
2016
Semidefinite characterization and computation of zero-dimensional real radical ideals. Zbl 1176.14010
Lasserre, Jean Bernard; Laurent, Monique; Rostalski, Philipp
2008
Generalized sampling and infinite-dimensional compressed sensing. Zbl 1379.94026
2016
Approximation methods for supervised learning. Zbl 1146.62322
DeVore, Ronald; Kerkyacharian, Gerard; Picard, Dominique; Temlyakov, Vladimir
2006
Online learning algorithms. Zbl 1119.68098
Smale, Steve; Yao, Yuan
2006
Direct and inverse Sobolev error estimates for scattered data interpolation via spherical basis functions. Zbl 1348.41010
Narcowich, Francis J.; Sun, Xingping; Ward, Joseph D.; Wendland, Holger
2007
Metrics for generalized persistence modules. Zbl 1345.55006
Bubenik, Peter; de Silva, Vin; Scott, Jonathan
2015
Combinatorial sublinear-time Fourier algorithms. Zbl 1230.65145
Iwen, M. A.
2010
Extending persistence using Poincaré and Lefschetz duality. Zbl 1189.55002
Cohen-Steiner, David; Edelsbrunner, Herbert; Harer, John
2009
On post-Lie algebras, Lie-Butcher series and moving frames. Zbl 1327.17001
Munthe-Kaas, Hans Z.; Lundervold, Alexander
2013
A conjecture on exceptional orthogonal polynomials. Zbl 1282.33019
Gómez-Ullate, David; Kamran, Niky; Milson, Robert
2013
Quadratic Newton iteration for systems with multiplicity. Zbl 1030.65050
Lecerf, G.
2002
Rigorous numerics for dissipative partial differential equations. II: Periodic orbit for the Kuramoto-Sivashinsky PDE – a computer-assisted proof. Zbl 1066.65105
Zgliczyński, Piotr
2004
The existence of Shilnikov homoclinic orbits in the Michelson system: A computer assisted proof. Zbl 1130.37415
Wilczak, Daniel
2006
Adaptive mollifiers for high resolution recovery of piecewise smooth data from its spectral information. Zbl 1056.42002
2002
A variational complex for difference equations. Zbl 1057.39013
Hydon, Peter E.; Mansfield, Elizabeth L.
2004
The number of singular vector tuples and uniqueness of best rank-one approximation of tensors. Zbl 1326.15036
Friedland, Shmuel; Ottaviani, Giorgio
2014
Joint invariant signatures. Zbl 1001.53004
Olver, Peter J.
2001
Improved bounds on sample size for implicit matrix trace estimators. Zbl 1323.65043
Roosta-Khorasani, Farbod; Ascher, Uri
2015
On the numerical stability of Fourier extensions. Zbl 1298.65198
Adcock, Ben; Huybrechs, Daan; Martín-Vaquero, Jesús
2014
A Riemannian view on shape optimization. Zbl 1296.49037
Schulz, Volker H.
2014
Error estimates for spectral convergence of the graph Laplacian on random geometric graphs toward the Laplace-Beltrami operator. Zbl 1447.62141
García Trillos, Nicolás; Gerlach, Moritz; Hein, Matthias; Slepčev, Dejan
2020
Splitting integrators for nonlinear Schrödinger equations over long times. Zbl 1189.65301
Gauckler, Ludwig; Lubich, Christian
2010
Numerical analysis of a robust free energy diminishing finite volume scheme for parabolic equations with gradient structure. Zbl 1382.65267
Cancès, Clément; Guichard, Cindy
2017
Low regularity exponential-type integrators for semilinear Schrödinger equations. Zbl 1402.65098
Ostermann, Alexander; Schratz, Katharina
2018
On local convergence of the method of alternating projections. Zbl 1339.65079
Noll, Dominikus; Rondepierre, Aude
2016
Convergence of fixed-point continuation algorithms for matrix rank minimization. Zbl 1219.90195
Goldfarb, Donald; Ma, Shiqian
2011
Gromov-Wasserstein distances and the metric approach to object matching. Zbl 1244.68078
Mémoli, Facundo
2011
Complexity of Bezout’s theorem. VI: Geodesics in the condition (number) metric. Zbl 1175.65060
Shub, Michael
2009
The Hopf algebra of rooted trees, free Lie algebras, and Lie series. Zbl 1116.17004
Murua, A.
2006
Tractability of approximation for weighted Korobov spaces on classical and quantum computers. Zbl 1072.81014
Novak, Erich; Sloan, Ian H.; Woźniakowski, Henryk
2004
Finding hidden cliques of size $$\sqrt{N/e}$$ in nearly linear time. Zbl 1347.05227
Deshpande, Yash; Montanari, Andrea
2015
Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients: a survey of analysis and implementation. Zbl 1362.65015
Kuo, Frances Y.; Nuyens, Dirk
2016
Fast linear homotopy to find approximate zeros of polynomial systems. Zbl 1232.65075
Beltrán, Carlos; Pardo, Luis Miguel
2011
A semidefinite approach for truncated $$K$$-moment problems. Zbl 1259.44005
Helton, J. William; Nie, Jiawang
2012
Rigorous computer-assisted application of KAM theory: a modern approach. Zbl 1383.37047
Figueras, J.-Ll.; Haro, A.; Luque, A.
2017
Sliding windows and persistence: an application of topological methods to signal analysis. Zbl 1325.37054
Perea, Jose A.; Harer, John
2015
The computational complexity of the Chow form. Zbl 1058.14075
Jeronimo, Gabriela; Krick, Teresa; Sabia, Juan; Sombra, Martín
2004
Parabolic molecules. Zbl 1403.42038
Grohs, Philipp; Kutyniok, Gitta
2014
Adaptive kernel methods using the balancing principle. Zbl 1204.68154
De Vito, E.; Pereverzyev, S.; Rosasco, L.
2010
Stochastic subgradient method converges on tame functions. Zbl 1433.65141
Davis, Damek; Drusvyatskiy, Dmitriy; Kakade, Sham; Lee, Jason D.
2020
A theoretical and empirical comparison of gradient approximations in derivative-free optimization. Zbl 07533997
Berahas, Albert S.; Cao, Liyuan; Choromanski, Krzysztof; Scheinberg, Katya
2022
On randomized trace estimates for indefinite matrices with an application to determinants. Zbl 07536706
Cortinovis, Alice; Kressner, Daniel
2022
Primal dual methods for Wasserstein gradient flows. Zbl 07533993
Carrillo, José A.; Craig, Katy; Wang, Li; Wei, Chaozhen
2022
A new upper bound for sampling numbers. Zbl 07533994
Nagel, Nicolas; Schäfer, Martin; Ullrich, Tino
2022
A counter-example to Hausmann’s conjecture. Zbl 07533995
Virk, Žiga
2022
Convergence of adaptive discontinuous Galerkin and $$C^0$$-interior penalty finite element methods for Hamilton-Jacobi-Bellman and Isaacs equations. Zbl 1492.65314
Kawecki, Ellya L.; Smears, Iain
2022
Proximal methods avoid active strict saddles of weakly convex functions. Zbl 07533998
Davis, Damek; Drusvyatskiy, Dmitriy
2022
Optimal stable nonlinear approximation. Zbl 07536699
Cohen, Albert; DeVore, Ronald; Petrova, Guergana; Wojtaszczyk, Przemyslaw
2022
Cumulant-cumulant relations in free probability theory from Magnus’ expansion. Zbl 07536702
Celestino, Adrian; Ebrahimi-Fard, Kurusch; Patras, Frédéric; Perales, Daniel
2022
Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities. Zbl 07568620
Hutzenthaler, Martin; Jentzen, Arnulf; Kruse, Thomas
2022
Kurdyka-Łojasiewicz exponent via inf-projection. Zbl 07568625
Yu, Peiran; Li, Guoyin; Pong, Ting Kei
2022
Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity. Zbl 1486.65208
Ostermann, Alexander; Rousset, Frédéric; Schratz, Katharina
2021
Function values are enough for $$L_2$$-approximation. Zbl 1481.41014
Krieg, David; Ullrich, Mario
2021
Topological properties of the set of functions generated by neural networks of fixed size. Zbl 07356508
Petersen, Philipp; Raslan, Mones; Voigtlaender, Felix
2021
Newton polytopes and relative entropy optimization. Zbl 1483.90121
Murray, Riley; Chandrasekaran, Venkat; Wierman, Adam
2021
Complexes from complexes. Zbl 07458824
Arnold, Douglas N.; Hu, Kaibo
2021
Sparse harmonic transforms: a new class of sublinear-time algorithms for learning functions of many variables. Zbl 1472.65171
Choi, Bosu; Iwen, Mark A.; Krahmer, Felix
2021
Primary ideals and their differential equations. Zbl 07434418
Cid-Ruiz, Yairon; Homs, Roser; Sturmfels, Bernd
2021
The Reeb graph edit distance is universal. Zbl 1485.55006
Bauer, Ulrich; Landi, Claudia; Mémoli, Facundo
2021
Low-rank matrix recovery with composite optimization: good conditioning and rapid convergence. Zbl 1480.65100
Charisopoulos, Vasileios; Chen, Yudong; Davis, Damek; Díaz, Mateo; Ding, Lijun; Drusvyatskiy, Dmitriy
2021
A neural network-based policy iteration algorithm with global $$H^2$$-superlinear convergence for stochastic games on domains. Zbl 1472.82030
Ito, Kazufumi; Reisinger, Christoph; Zhang, Yufei
2021
Weak convergence rates for Euler-type approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients. Zbl 1482.65143
Jentzen, Arnulf; Kurniawan, Ryan
2021
Wavenumber-explicit hp-FEM analysis for Maxwell’s equations with transparent boundary conditions. Zbl 1460.35085
Melenk, Jens M.; Sauter, Stefan A.
2021
Data analysis from empirical moments and the Christoffel function. Zbl 1461.62234
Pauwels, Edouard; Putinar, Mihai; Lasserre, Jean-Bernard
2021
Towards massively parallel computations in algebraic geometry. Zbl 1485.14109
Böhm, Janko; Decker, Wolfram; Frühbis-Krüger, Anne; Pfreundt, Franz-Josef; Rahn, Mirko; Ristau, Lukas
2021
On the complexity exponent of polynomial system solving. Zbl 1457.14002
van der Hoeven, Joris; Lecerf, Grégoire
2021
Perturbations of Christoffel-Darboux kernels: detection of outliers. Zbl 1470.42049
Beckermann, Bernhard; Putinar, Mihai; Saff, Edward B.; Stylianopoulos, Nikos
2021
On the convergence of time splitting methods for quantum dynamics in the semiclassical regime. Zbl 1471.65038
Golse, François; Jin, Shi; Paul, Thierry
2021
Numerical performance of optimized Frolov lattices in tensor product reproducing kernel Sobolev spaces. Zbl 1480.46037
Kacwin, Christopher; Oettershagen, Jens; Ullrich, Mario; Ullrich, Tino
2021
A variational finite element discretization of compressible flow. Zbl 07404750
Gawlik, Evan S.; Gay-Balmaz, François
2021
Convergence rates for discretized Monge-Ampère equations and quantitative stability of optimal transport. Zbl 1475.35151
Berman, Robert J.
2021
Computing the homology of semialgebraic sets. II: General formulas. Zbl 1492.14103
Bürgisser, Peter; Cucker, Felipe; Tonelli-Cueto, Josué
2021
Metrics, quantization and registration in varifold spaces. Zbl 1477.49066
Hsieh, Hsi-Wei; Charon, Nicolas
2021
Fenchel duality theory and a primal-dual algorithm on Riemannian manifolds. Zbl 07458819
Bergmann, Ronny; Herzog, Roland; Silva Louzeiro, Maurício; Tenbrinck, Daniel; Vidal-Núñez, José
2021
The Grassmannian of affine subspaces. Zbl 1485.14096
Lim, Lek-Heng; Wong, Ken Sze-Wai; Ye, Ke
2021
Noncommutative polynomials describing convex sets. Zbl 1471.14120
Helton, J. William; Klep, Igor; McCullough, Scott; Volčič, Jurij
2021
Real quadratic Julia sets can have arbitrarily high complexity. Zbl 07326846
Rojas, Cristobal; Yampolsky, Michael
2021
A unifying representer theorem for inverse problems and machine learning. Zbl 1479.46088
Unser, Michael
2021
Computing higher Leray-Serre spectral sequences of towers of fibrations. Zbl 1483.18027
Guidolin, Andrea; Romero, Ana
2021
Curve based approximation of measures on manifolds by discrepancy minimization. Zbl 1491.65048
Ehler, Martin; Gräf, Manuel; Neumayer, Sebastian; Steidl, Gabriele
2021
Error estimates for spectral convergence of the graph Laplacian on random geometric graphs toward the Laplace-Beltrami operator. Zbl 1447.62141
García Trillos, Nicolás; Gerlach, Moritz; Hein, Matthias; Slepčev, Dejan
2020
Stochastic subgradient method converges on tame functions. Zbl 1433.65141
Davis, Damek; Drusvyatskiy, Dmitriy; Kakade, Sham; Lee, Jason D.
2020
Implicit regularization in nonconvex statistical estimation: gradient descent converges linearly for phase retrieval, matrix completion, and blind deconvolution. Zbl 1445.90089
Ma, Cong; Wang, Kaizheng; Chi, Yuejie; Chen, Yuxin
2020
On the sample complexity of the linear quadratic regulator. Zbl 1447.49052
Dean, Sarah; Mania, Horia; Matni, Nikolai; Recht, Benjamin; Tu, Stephen
2020
Operator scaling: theory and applications. Zbl 1432.68617
Garg, Ankit; Gurvits, Leonid; Oliveira, Rafael; Wigderson, Avi
2020
A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations. Zbl 07161200
Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles
2020
Stability of low-rank tensor representations and structured multilevel preconditioning for elliptic PDEs. Zbl 1454.65160
2020
Convergence analysis of deterministic kernel-based quadrature rules in misspecified settings. Zbl 07161204
Kanagawa, Motonobu; Sriperumbudur, Bharath K.; Fukumizu, Kenji
2020
Computing the interleaving distance is NP-hard. Zbl 1460.55006
Bjerkevik, Håvard Bakke; Botnan, Magnus Bakke; Kerber, Michael
2020
Computing tropical varieties over fields with valuation. Zbl 1445.14085
Markwig, Thomas; Ren, Yue
2020
Convergence of finite volume schemes for the Euler equations via dissipative measure-valued solutions. Zbl 1447.65050
Feireisl, Eduard; Lukáčová-Medvid&rsquo;ová, Mária; Mizerová, Hana
2020
Linking combinatorial and classical dynamics: Conley index and Morse decompositions. Zbl 1456.37040
Batko, Bogdan; Kaczynski, Tomasz; Mrozek, Marian; Wanner, Thomas
2020
Multisymplecticity of hybridizable discontinuous Galerkin methods. Zbl 1472.65147
Mclachlan, Robert I.; Stern, Ari
2020
Computing the homology of semialgebraic sets. I: Lax formulas. Zbl 1440.14264
Bürgisser, Peter; Cucker, Felipe; Tonelli-Cueto, Josué
2020
Local cohomology and stratification. Zbl 1439.55005
Nanda, Vidit
2020
The real polynomial eigenvalue problem is well conditioned on the average. Zbl 1472.14068
Beltrán, Carlos; Kozhasov, Khazhgali
2020
Certifying global optimality of graph cuts via semidefinite relaxation: a performance guarantee for spectral clustering. Zbl 1445.90109
Ling, Shuyang; Strohmer, Thomas
2020
On the convergence of the spectral viscosity method for the two-dimensional incompressible Euler equations with rough initial data. Zbl 1454.65125
Lanthaler, Samuel; Mishra, Siddhartha
2020
Effective models and numerical homogenization for wave propagation in heterogeneous media on arbitrary timescales. Zbl 1456.35015
Abdulle, Assyr; Pouchon, Timothée
2020
Mathematics of smoothed particle hydrodynamics: a study via nonlocal Stokes equations. Zbl 1448.76112
Du, Qiang; Tian, Xiaochuan
2020
Lie-Poisson methods for isospectral flows. Zbl 1450.37073
Modin, Klas; Viviani, Milo
2020
Geometry of matrix polynomial spaces. Zbl 1444.15007
Dmytryshyn, Andrii; Johansson, Stefan; Kågström, Bo; Van Dooren, Paul
2020
Reconstruction and interpolation of manifolds. I: The geometric Whitney problem. Zbl 1470.53045
Fefferman, Charles; Ivanov, Sergei; Kurylev, Yaroslav; Lassas, Matti; Narayanan, Hariharan
2020
Inverse potential problems for divergence of measures with total variation regularization. Zbl 1460.35077
Baratchart, L.; Villalobos Guillén, C.; Hardin, D. P.; Northington, M. C.; Saff, E. B.
2020
Wilkinson’s bus: weak condition numbers, with an application to singular polynomial eigenproblems. Zbl 1455.65056
Lotz, Martin; Noferini, Vanni
2020
On the minimal displacement vector of compositions and convex combinations of nonexpansive mappings. Zbl 07290668
Bauschke, Heinz H.; Moursi, Walaa M.
2020
Symbolic computations of first integrals for polynomial vector fields. Zbl 1485.34006
Chèze, Guillaume; Combot, Thierry
2020
Tropical combinatorial Nullstellensatz and sparse polynomials. Zbl 1455.14126
2020
Are two given maps homotopic? An algorithmic viewpoint. Zbl 1436.55020
Filakovský, M.; Vokřínek, L.
2020
Projective geometry of Wachspress coordinates. Zbl 1451.14131
2020
Preservation of bifurcations of Hamiltonian boundary value problems under discretisation. Zbl 1455.65114
McLachlan, Robert I.; Offen, Christian
2020
Propagation of one- and two-dimensional discrete waves under finite difference approximation. Zbl 1457.35009
Biccari, Umberto; Marica, Aurora; Zuazua, Enrique
2020
Analysis of artifacts in shell-based image inpainting: why they occur and how to eliminate them. Zbl 07290667
Hocking, L. Robert; Holding, Thomas; Schönlieb, Carola-Bibiane
2020
Correction to: “The complexity of factors of multivariate polynomials”. Zbl 1470.68046
Bürgisser, Peter
2020
Stable phase retrieval in infinite dimensions. Zbl 1440.94010
Alaifari, Rima; Daubechies, Ingrid; Grohs, Philipp; Yin, Rujie
2019
Mean estimation and regression under heavy-tailed distributions: A survey. Zbl 1431.62123
Lugosi, Gábor; Mendelson, Shahar
2019
Stable extrapolation of analytic functions. Zbl 1410.41001
Demanet, Laurent; Townsend, Alex
2019
Tensor FEM for spectral fractional diffusion. Zbl 1429.65272
Banjai, Lehel; Melenk, Jens M.; Nochetto, Ricardo H.; Otárola, Enrique; Salgado, Abner J.; Schwab, Christoph
2019
Efficient methods for the estimation of homogenized coefficients. Zbl 1411.82021
Mourrat, J.-C.
2019
Fundamental limits of weak recovery with applications to phase retrieval. Zbl 1464.62296
Mondelli, Marco; Montanari, Andrea
2019
On polynomial time methods for exact low-rank tensor completion. Zbl 1436.15031
Xia, Dong; Yuan, Ming
2019
Tropical coordinates on the space of persistence barcodes. Zbl 1423.55007
Kališnik, Sara
2019
Correction to: “On the stability and accuracy of least squares approximations”. Zbl 1407.93436
Cohen, Albert; Davenport, Mark A.; Leviatan, Dany
2019
Random bit quadrature and approximation of distributions on Hilbert spaces. Zbl 1432.60044
Giles, Michael B.; Hefter, Mario; Mayer, Lukas; Ritter, Klaus
2019
The geometry of gaussoids. Zbl 1453.13076
Boege, Tobias; D&rsquo;Alì, Alessio; Kahle, Thomas; Sturmfels, Bernd
2019
On the Dirac-Frenkel variational principle on tensor Banach spaces. Zbl 1427.46013
Falcó, Antonio; Hackbusch, Wolfgang; Nouy, Anthony
2019
Lower bounds on matrix factorization ranks via noncommutative polynomial optimization. Zbl 07118503
Gribling, Sander; de Laat, David; Laurent, Monique
2019
Orthogonal systems with a skew-symmetric differentiation matrix. Zbl 1428.42048
Iserles, Arieh; Webb, Marcus
2019
Rational invariants of even ternary forms under the orthogonal group. Zbl 1439.13019
Görlach, Paul; Hubert, Evelyne; Papadopoulo, Théo
2019
A geometric framework for stochastic shape analysis. Zbl 1422.60089
Arnaudon, Alexis; Holm, Darryl D.; Sommer, Stefan
2019
Probabilistic condition number estimates for real polynomial systems. I: A broader family of distributions. Zbl 1409.65033
Ergür, Alperen A.; Paouris, Grigoris; Rojas, J. Maurice
2019
Semidefinite approximations of the matrix logarithm. Zbl 1411.90254
Fawzi, Hamza; Saunderson, James; Parrilo, Pablo A.
2019
Improved complexity bounds for counting points on hyperelliptic curves. Zbl 1470.11170
Abelard, Simon; Gaudry, Pierrick; Spaenlehauer, Pierre-Jean
2019
Unified convergence analysis of numerical schemes for a miscible displacement problem. Zbl 1411.65109
Droniou, Jérôme; Eymard, Robert; Prignet, Alain; Talbot, Kyle S.
2019
On a randomized backward Euler method for nonlinear evolution equations with time-irregular coefficients. Zbl 07135262
Eisenmann, Monika; Kovács, Mihály; Kruse, Raphael; Larsson, Stig
2019
Complexity of sparse polynomial solving: homotopy on toric varieties and the condition metric. Zbl 1408.65032
Malajovich, Gregorio
2019
A polynomial rate of asymptotic regularity for compositions of projections in Hilbert space. Zbl 07027311
Kohlenbach, Ulrich
2019
Complexity classes and completeness in algebraic geometry. Zbl 1422.14065
Umut Isik, M.
2019
Solving equations of random convex functions via anchored regression. Zbl 1422.62235
Bahmani, Sohail; Romberg, Justin
2019
Variational discretizations of gauge field theories using group-equivariant interpolation. Zbl 1437.37110
Leok, Melvin
2019
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### Cited by 8,878 Authors

 53 Schwab, Christoph 46 Zhou, Dingxuan 38 Ballico, Edoardo 36 Praetorius, Dirk 32 Amat, Sergio P. 31 Wu, Xinyuan 28 Hauenstein, Jonathan D. 28 Lessard, Jean-Philippe 28 Temlyakov, Vladimir Nikolaevich 27 Ferreira, Orizon Pereira 27 Jentzen, Arnulf 25 Dahlke, Stephan 25 Mrozek, Marian 25 Nobile, Fabio 25 Wang, Bin 24 Chartier, Philippe 24 Nie, Jiawang 24 Stevenson, Rob P. 23 Rauhut, Holger 23 Woźniakowski, Henryk 22 Mireles-James, Jason D. 22 Mischaikow, Konstantin 22 Sturmfels, Bernd 22 Trillo, Juan Carlos 21 Carstensen, Carsten 21 Chen, Dirong 21 Cucker, Felipe 21 Kuo, Frances Y. 21 Mémoli, Facundo 21 Ullrich, Tino 21 Wasilkowski, Grzegorz W. 20 Adcock, Ben 20 Bernardi, Alessandra 20 Tropp, Joel A. 19 Lin, Shaobo 19 Nochetto, Ricardo Horacio 19 Sun, Hongwei 19 Xu, Zongben 18 Cai, Jian-Feng 18 Cao, Feilong 18 Fornasier, Massimo 17 Beltrán, Carlos 17 Bürgisser, Peter 17 Dick, Josef 17 Dinh Dũng 17 Fan, Jinyan 17 Grohs, Philipp 17 Krahmer, Felix 17 Landsberg, Joseph Montague 17 Leok, Melvin 17 Peyré, Gabriel 17 Rosasco, Lorenzo A. 17 Zgliczyński, Piotr 16 Cohen, Albert 16 Drusvyatskiy, Dmitriy 16 Ebrahimi-Fard, Kurusch 16 Harbrecht, Helmut 16 Iserles, Arieh 16 Iwen, Mark A. 16 Kutyniok, Gitta 16 Luke, David Russell 16 Manchon, Dominique 16 Narayan, Akil C. 16 Oliveira, Paulo Roberto 16 Pardo, Luis Miguel 16 Romani, Lucia 16 Schneider, Reinhold 16 Sloan, Ian Hugh 15 Dahmen, Wolfgang A. 15 Dyn, Nira 15 Hu, Ting 15 Huybrechs, Daan 15 Liandrat, Jacques 15 Michałek, Mateusz 15 Murua, Ander 15 Pilarczyk, Paweł 15 Ritter, Klaus 15 Schratz, Katharina 15 Tempone, Raúl F. 15 Wen, Zaiwen 15 Zou, Bin 14 Absil, Pierre-Antoine 14 Cevher, Volkan 14 Conti, Costanza 14 Fadili, Jalal M. 14 Feireisl, Eduard 14 Guo, Zheng-Chu 14 Kruger, Alexander Y. 14 Li, Song 14 Lim, Lek-Heng 14 Méhats, Florian 14 Mourrain, Bernard 14 Otárola, Enrique 14 Pong, Ting Kei 14 Protasov, Vladimir Yu. 14 Sickel, Winfried 14 van den Berg, Jan Bouwe 14 Wei, Ke 14 Wu, Qiang 14 Xiang, Dao-Hong ...and 8,778 more Authors
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### Cited in 656 Journals

 261 Foundations of Computational Mathematics 173 Applied and Computational Harmonic Analysis 167 Mathematics of Computation 146 Numerische Mathematik 136 SIAM Journal on Numerical Analysis 136 Journal of Complexity 131 SIAM Journal on Scientific Computing 125 Linear Algebra and its Applications 124 SIAM Journal on Optimization 121 Mathematical Programming. Series A. Series B 120 Journal of Computational Physics 117 Journal of Computational and Applied Mathematics 115 Journal of Scientific Computing 106 Journal of Symbolic Computation 91 The Annals of Statistics 91 Applied Mathematics and Computation 91 Advances in Computational Mathematics 87 Journal of Approximation Theory 72 Journal of Machine Learning Research (JMLR) 71 Computational Optimization and Applications 71 SIAM Journal on Imaging Sciences 68 Journal of Optimization Theory and Applications 68 Numerical Algorithms 65 Computers & Mathematics with Applications 63 Applied Numerical Mathematics 60 Discrete & Computational Geometry 59 Journal of Mathematical Analysis and Applications 57 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 56 Constructive Approximation 54 SIAM Journal on Matrix Analysis and Applications 51 Electronic Journal of Statistics 50 Inverse Problems 49 Computer Methods in Applied Mechanics and Engineering 48 Journal of Mathematical Imaging and Vision 48 The Journal of Fourier Analysis and Applications 47 SIAM Journal on Applied Dynamical Systems 45 Advances in Mathematics 45 BIT 44 SIAM Journal on Applied Algebra and Geometry 43 Analysis and Applications (Singapore) 42 SIAM Journal on Mathematics of Data Science 40 SIAM/ASA Journal on Uncertainty Quantification 40 Journal of Applied and Computational Topology 39 Journal of Mathematical Physics 39 Physica D 38 Journal of Global Optimization 36 International Journal of Wavelets, Multiresolution and Information Processing 34 Journal of Differential Equations 33 Science China. Mathematics 32 Communications in Mathematical Physics 31 Bernoulli 30 Machine Learning 30 Discrete and Continuous Dynamical Systems 29 Automatica 28 Calcolo 27 Nonlinearity 27 International Journal of Computer Vision 26 Theoretical Computer Science 26 Neural Computation 26 Computational Methods in Applied Mathematics 23 Journal of Algebra 23 Journal of Pure and Applied Algebra 23 International Journal of Computer Mathematics 23 SIAM Journal on Mathematical Analysis 23 Multiscale Modeling & Simulation 22 Linear and Multilinear Algebra 22 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 22 Abstract and Applied Analysis 21 Acta Applicandae Mathematicae 21 Set-Valued and Variational Analysis 21 Journal of Computational Dynamics 20 Optimization Methods & Software 20 Journal of Inequalities and Applications 20 Discrete and Continuous Dynamical Systems. Series B 20 Optimization Letters 19 Bulletin of Mathematical Biology 19 Advances in Applied Mathematics 19 Computer Aided Geometric Design 19 SIAM Review 19 Information and Inference 18 Information Sciences 18 Proceedings of the American Mathematical Society 18 SIAM Journal on Control and Optimization 18 Japan Journal of Industrial and Applied Mathematics 18 Vietnam Journal of Mathematics 17 Journal of Geometry and Physics 17 Mathematics of Operations Research 17 Neural Networks 17 Communications in Nonlinear Science and Numerical Simulation 17 Inverse Problems and Imaging 16 Archive for Rational Mechanics and Analysis 16 Journal of Functional Analysis 16 SIAM Journal on Computing 16 Journal of Nonlinear Science 16 Mathematics in Computer Science 16 Statistics and Computing 15 Mathematische Zeitschrift 15 Optimization 14 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 14 Transactions of the American Mathematical Society ...and 556 more Journals
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### Cited in 62 Fields

 3,135 Numerical analysis (65-XX) 1,204 Computer science (68-XX) 1,159 Operations research, mathematical programming (90-XX) 1,054 Partial differential equations (35-XX) 933 Statistics (62-XX) 704 Linear and multilinear algebra; matrix theory (15-XX) 567 Information and communication theory, circuits (94-XX) 551 Approximations and expansions (41-XX) 519 Probability theory and stochastic processes (60-XX) 518 Algebraic geometry (14-XX) 475 Dynamical systems and ergodic theory (37-XX) 475 Calculus of variations and optimal control; optimization (49-XX) 353 Harmonic analysis on Euclidean spaces (42-XX) 350 Ordinary differential equations (34-XX) 261 Operator theory (47-XX) 251 Functional analysis (46-XX) 245 Algebraic topology (55-XX) 227 Fluid mechanics (76-XX) 209 Commutative algebra (13-XX) 200 Biology and other natural sciences (92-XX) 194 Combinatorics (05-XX) 189 Differential geometry (53-XX) 179 Global analysis, analysis on manifolds (58-XX) 170 Convex and discrete geometry (52-XX) 152 Systems theory; control (93-XX) 146 Quantum theory (81-XX) 138 Mechanics of particles and systems (70-XX) 137 Number theory (11-XX) 104 Mechanics of deformable solids (74-XX) 99 Real functions (26-XX) 94 Field theory and polynomials (12-XX) 92 Manifolds and cell complexes (57-XX) 91 Statistical mechanics, structure of matter (82-XX) 88 Functions of a complex variable (30-XX) 84 Optics, electromagnetic theory (78-XX) 83 Special functions (33-XX) 79 Associative rings and algebras (16-XX) 68 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 66 Nonassociative rings and algebras (17-XX) 60 Difference and functional equations (39-XX) 43 Mathematical logic and foundations (03-XX) 42 Group theory and generalizations (20-XX) 39 Topological groups, Lie groups (22-XX) 39 Several complex variables and analytic spaces (32-XX) 39 Geometry (51-XX) 38 Integral equations (45-XX) 37 Measure and integration (28-XX) 35 General topology (54-XX) 34 Category theory; homological algebra (18-XX) 33 Integral transforms, operational calculus (44-XX) 28 Potential theory (31-XX) 24 Geophysics (86-XX) 22 General and overarching topics; collections (00-XX) 19 Order, lattices, ordered algebraic structures (06-XX) 18 Classical thermodynamics, heat transfer (80-XX) 14 History and biography (01-XX) 13 Abstract harmonic analysis (43-XX) 7 Relativity and gravitational theory (83-XX) 4 General algebraic systems (08-XX) 3 Sequences, series, summability (40-XX) 2 Astronomy and astrophysics (85-XX) 1 $$K$$-theory (19-XX)