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## Walther, Andrea

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 Author ID: walther.andrea Published as: Walther, A.; Walther, Andrea External Links: Wikidata · ORCID · GND
 Documents Indexed: 67 Publications since 1999, including 3 Books Reviewing Activity: 37 Reviews
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#### Co-Authors

 9 single-authored 23 Griewank, Andreas 6 Schlenkrich, Sebastian 5 Gauger, Nicolas R. 4 Herzog, Roland 4 Stumm, Philipp 3 Biegler, Lorenz T. 3 Fiege, Sabrina 3 Gebremedhin, Assefaw Hadish 3 Kulshreshtha, Kshitij 3 Kusch, Lisa 3 Pothen, Alex 2 Banović, Mladen 2 Kowarz, Andreas 2 Lehmann, Uwe 2 Moldenhauer, Carsten 2 Naumann, Uwe 2 Riehme, Jan 2 Utke, Jean 2 Vogel, Olaf 1 Albring, Tim 1 Auriemma, Salvatore 1 Best, André 1 Bischof, Christian H. 1 Bock, Hans Georg 1 Bosse, Torsten 1 Claes, Leander 1 Diehl, Moritz Mathias 1 Eppler, Karsten 1 Forth, Shaun A. 1 Guertler, Niels 1 Harbrecht, Helmut 1 Henning, Bernd 1 Holfeld, Denise 1 Hovland, Paul D. 1 Jurgelucks, Benjamin 1 Klein, Wolfram 1 Korzec, Maciek D. 1 Kostina, Ekaterina A. 1 Legrand, Herve 1 Letschert, Benjamin 1 Meyer, Marcus 1 Müller, Jens-Dominik 1 Mykhaskiv, Orest 1 Nguyen, Duc Dung 1 Noack, Antje 1 Özkaya, Emre 1 Phipps, Eric T. 1 Richert, Natalie 1 Schaefer, Bernd-Jochen 1 Schmidt, Stephan 1 Schütte, Maria 1 Stiller, Jörg 1 Tarafdar, Arijit 1 Vasilopoulos, Ilias 1 Vetukuri, Sree Rama Raju 1 Wagner, Mathias 1 Widhalm, Markus
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#### Serials

 13 Optimization Methods & Software 5 PAMM. Proceedings in Applied Mathematics and Mechanics 4 Computational Optimization and Applications 3 Mathematical Programming. Series A. Series B 3 SIAM Journal on Optimization 3 SIAM Journal on Scientific Computing 2 ACM Transactions on Mathematical Software 2 Computing 2 Applied Numerical Mathematics 2 Optimization and Engineering 1 Acta Informatica 1 Computer Physics Communications 1 Mathematics of Computation 1 Journal of Optimization Theory and Applications 1 Optimal Control Applications & Methods 1 Revista Investigación Operacional 1 INFORMS Journal on Computing 1 Vietnam Journal of Mathematics 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Journal of Mathematical Study 1 Discussiones Mathematicae. Differential Inclusions, Control and Optimization 1 Lecture Notes in Computational Science and Engineering
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#### Fields

 43 Numerical analysis (65-XX) 28 Operations research, mathematical programming (90-XX) 23 Calculus of variations and optimal control; optimization (49-XX) 21 Computer science (68-XX) 4 Fluid mechanics (76-XX) 2 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Partial differential equations (35-XX) 2 Mechanics of particles and systems (70-XX) 2 Mechanics of deformable solids (74-XX) 2 Optics, electromagnetic theory (78-XX) 2 Systems theory; control (93-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Integral equations (45-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX)

#### Citations contained in zbMATH

41 Publications have been cited 496 times in 363 Documents Cited by Year
Evaluating derivatives. Principles and techniques of algorithmic differentiation. 2nd ed. Zbl 1159.65026
Griewank, Andreas; Walther, Andrea
2008
Algorithm 799: revolve: an implementation of checkpointing for the reverse or adjoint mode of computational differentiation. Zbl 1137.65330
Griewank, Andreas; Walther, Andrea
2000
Efficient computation of sparse hessians using coloring and automatic differentiation. Zbl 1243.65071
Gebremedhin, Assefaw H.; Tarafdar, Arijit; Pothen, Alex; Walther, Andrea
2009
Evaluating higher derivative tensors by forward propagation of univariate Taylor series. Zbl 0952.65028
Griewank, Andreas; Utke, Jean; Walther, Andrea
2000
Automatic differentiation of explicit Runge-Kutta methods for optimal control. Zbl 1278.49037
Walther, Andrea
2007
On constrained optimization by adjoint based quasi-Newton methods. Zbl 1065.90077
Griewank, Andreas; Walther, Andrea
2002
First- and second-order optimality conditions for piecewise smooth objective functions. Zbl 1385.90026
Griewank, A.; Walther, A.
2016
Adjoint concepts for the optimal control of Burgers equation. Zbl 1278.49028
Noack, Antje; Walther, Andrea
2007
On Lipschitz optimization based on gray-box piecewise linearization. Zbl 1350.49038
Griewank, Andreas; Walther, Andrea; Fiege, Sabrina; Bosse, Torsten
2016
Evaluating gradients in optimal control: continuous adjoints versus automatic differentiation. Zbl 1130.49308
Griesse, R.; Walther, A.
2004
New algorithms for optimal online checkpointing. Zbl 1214.65038
Stumm, Philipp; Walther, Andrea
2010
Multistage approaches for optimal offline checkpointing. Zbl 1194.65084
Stumm, Philipp; Walther, Andrea
2009
Parametric sensitivities for optimal control problems using automatic differentiation. Zbl 1073.93518
Griesse, Roland; Walther, Andrea
2003
An adjoint-based SQP algorithm with quasi-Newton Jacobian updates for inequality constrained optimization. Zbl 1197.49034
Diehl, Moritz; Walther, Andrea; Bock, Hans Georg; Kostina, Ekaterina
2010
On the local convergence of adjoint Broyden methods. Zbl 1185.90207
Schlenkrich, Sebastian; Griewank, Andreas; Walther, Andrea
2010
Maintaining factorized KKT systems subject to rank-one updates of Hessians and Jacobians. Zbl 1196.90130
Griewank, Andreas; Walther, Andrea; Korzec, Maciek
2007
Recent advances in algorithmic differentiation. Selected papers based on the presentations at the 6th international conference on automatic differentiation (AD2012), Fort Collins, CO, USA, July 23–27, 2012. Zbl 1247.65002
Forth, Shaun (ed.); Hovland, Paul (ed.); Phipps, Eric (ed.); Utke, Jean (ed.); Walther, Andrea (ed.)
2012
On the numerical stability of algorithmic differentiation. Zbl 1238.65013
Griewank, Andreas; Kulshreshtha, Kshitij; Walther, Andrea
2012
Numerical experiments with an inexact Jacobian trust-region algorithm. Zbl 1219.90166
Walther, Andrea; Biegler, Lorenz T.
2011
On the efficient computation of high-order derivatives for implicitly defined functions. Zbl 1205.65131
Wagner, Mathias; Walther, Andrea; Schaefer, Bernd-Jochen
2010
Global convergence of quasi-Newton methods based on adjoint Broyden updates. Zbl 1163.65025
Schlenkrich, Sebastian; Walther, Andrea
2009
Computing sparse Hessians with automatic differentiation. Zbl 1291.65190
Walther, Andrea
2008
Application of AD-based quasi-Newton methods to stiff ODEs. Zbl 1270.65035
Schlenkrich, Sebastian; Walther, Andrea; Griewank, Andreas
2006
Walther, Andrea; Griewank, Andreas
2004
On an extension of one-shot methods to incorporate additional constraints. Zbl 1369.49041
Walther, Andrea; Gauger, Nicolas R.; Kusch, Lisa; Richert, Natalie
2016
A first-order convergence analysis of trust-region methods with inexact Jacobians. Zbl 1163.90028
Walther, Andrea
2008
Optimal $$r$$-order of an adjoint Broyden method without the assumption of linearly independent steps. Zbl 1211.90291
Griewank, Andreas; Schlenkrich, Sebastian; Walther, Andrea
2008
Walther, Andrea; Griewank, Andreas; Vogel, Olaf
2003
Characterizing and testing subdifferential regularity in piecewise smooth optimization. Zbl 1422.49016
Walther, Andrea; Griewank, Andreas
2019
Relaxing kink qualifications and proving convergence rates in piecewise smooth optimization. Zbl 1410.90252
Griewank, Andreas; Walther, Andrea
2019
Algorithmic differentiation for piecewise smooth functions: a case study for robust optimization. Zbl 1401.90168
Fiege, Sabrina; Walther, Andrea; Kulshreshtha, Kshitij; Griewank, Andreas
2018
On the efficient computation of sparsity patterns for Hessians. Zbl 1251.65037
Walther, Andrea
2012
A first-order convergence analysis of trust-region methods with inexact Jacobians and inequality constraints. Zbl 1242.90244
Walther, Andrea; Vetukuri, Sree Rama Raju; Biegler, Lorenz T.
2012
Towards matrix-free AD-based preconditioning of KKT systems in PDE-constrained optimization. Zbl 1391.65153
Griesse, Roland; Walther, Andrea
2005
Algorithmic differentiation of the Open CASCADE technology CAD kernel and its coupling with an adjoint CFD solver. Zbl 1408.90321
Banović, Mladen; Mykhaskiv, Orest; Auriemma, Salvatore; Walther, Andrea; Legrand, Herve; Müller, Jens-Dominik
2018
On an inexact trust-region SQP-filter method for constrained nonlinear optimization. Zbl 1362.90344
Walther, Andrea; Biegler, Lorenz
2016
Exploiting sparsity in Jacobian computation via coloring and automatic differentiation: A case study in a simulated moving bed process. Zbl 1152.65416
Gebremedhin, Assefaw H.; Pothen, Alex; Walther, Andrea
2008
Automatic differentiation of an entire design chain for aerodynamic shape optimization. Zbl 1409.76126
Gauger, Nicolas R.; Walther, Andrea; Moldenhauer, Carsten; Widhalm, Markus
2007
Bounding the number of processors and checkpoints needed in time-minimal parallel reversal schedules. Zbl 1102.68417
Walther, A.
2004
Introduction to automatic differentiation. Zbl 1201.68160
Griewank, Andreas; Walther, Andrea
2003
The implementation and testing of time-minimal and resource-optimal parallel reversal schedules. Zbl 1055.68526
Lehmann, U.; Walther, A.
2002
Characterizing and testing subdifferential regularity in piecewise smooth optimization. Zbl 1422.49016
Walther, Andrea; Griewank, Andreas
2019
Relaxing kink qualifications and proving convergence rates in piecewise smooth optimization. Zbl 1410.90252
Griewank, Andreas; Walther, Andrea
2019
Algorithmic differentiation for piecewise smooth functions: a case study for robust optimization. Zbl 1401.90168
Fiege, Sabrina; Walther, Andrea; Kulshreshtha, Kshitij; Griewank, Andreas
2018
Algorithmic differentiation of the Open CASCADE technology CAD kernel and its coupling with an adjoint CFD solver. Zbl 1408.90321
Banović, Mladen; Mykhaskiv, Orest; Auriemma, Salvatore; Walther, Andrea; Legrand, Herve; Müller, Jens-Dominik
2018
First- and second-order optimality conditions for piecewise smooth objective functions. Zbl 1385.90026
Griewank, A.; Walther, A.
2016
On Lipschitz optimization based on gray-box piecewise linearization. Zbl 1350.49038
Griewank, Andreas; Walther, Andrea; Fiege, Sabrina; Bosse, Torsten
2016
On an extension of one-shot methods to incorporate additional constraints. Zbl 1369.49041
Walther, Andrea; Gauger, Nicolas R.; Kusch, Lisa; Richert, Natalie
2016
On an inexact trust-region SQP-filter method for constrained nonlinear optimization. Zbl 1362.90344
Walther, Andrea; Biegler, Lorenz
2016
Recent advances in algorithmic differentiation. Selected papers based on the presentations at the 6th international conference on automatic differentiation (AD2012), Fort Collins, CO, USA, July 23–27, 2012. Zbl 1247.65002
Forth, Shaun (ed.); Hovland, Paul (ed.); Phipps, Eric (ed.); Utke, Jean (ed.); Walther, Andrea (ed.)
2012
On the numerical stability of algorithmic differentiation. Zbl 1238.65013
Griewank, Andreas; Kulshreshtha, Kshitij; Walther, Andrea
2012
On the efficient computation of sparsity patterns for Hessians. Zbl 1251.65037
Walther, Andrea
2012
A first-order convergence analysis of trust-region methods with inexact Jacobians and inequality constraints. Zbl 1242.90244
Walther, Andrea; Vetukuri, Sree Rama Raju; Biegler, Lorenz T.
2012
Numerical experiments with an inexact Jacobian trust-region algorithm. Zbl 1219.90166
Walther, Andrea; Biegler, Lorenz T.
2011
New algorithms for optimal online checkpointing. Zbl 1214.65038
Stumm, Philipp; Walther, Andrea
2010
An adjoint-based SQP algorithm with quasi-Newton Jacobian updates for inequality constrained optimization. Zbl 1197.49034
Diehl, Moritz; Walther, Andrea; Bock, Hans Georg; Kostina, Ekaterina
2010
On the local convergence of adjoint Broyden methods. Zbl 1185.90207
Schlenkrich, Sebastian; Griewank, Andreas; Walther, Andrea
2010
On the efficient computation of high-order derivatives for implicitly defined functions. Zbl 1205.65131
Wagner, Mathias; Walther, Andrea; Schaefer, Bernd-Jochen
2010
Efficient computation of sparse hessians using coloring and automatic differentiation. Zbl 1243.65071
Gebremedhin, Assefaw H.; Tarafdar, Arijit; Pothen, Alex; Walther, Andrea
2009
Multistage approaches for optimal offline checkpointing. Zbl 1194.65084
Stumm, Philipp; Walther, Andrea
2009
Global convergence of quasi-Newton methods based on adjoint Broyden updates. Zbl 1163.65025
Schlenkrich, Sebastian; Walther, Andrea
2009
Evaluating derivatives. Principles and techniques of algorithmic differentiation. 2nd ed. Zbl 1159.65026
Griewank, Andreas; Walther, Andrea
2008
Computing sparse Hessians with automatic differentiation. Zbl 1291.65190
Walther, Andrea
2008
A first-order convergence analysis of trust-region methods with inexact Jacobians. Zbl 1163.90028
Walther, Andrea
2008
Optimal $$r$$-order of an adjoint Broyden method without the assumption of linearly independent steps. Zbl 1211.90291
Griewank, Andreas; Schlenkrich, Sebastian; Walther, Andrea
2008
Exploiting sparsity in Jacobian computation via coloring and automatic differentiation: A case study in a simulated moving bed process. Zbl 1152.65416
Gebremedhin, Assefaw H.; Pothen, Alex; Walther, Andrea
2008
Automatic differentiation of explicit Runge-Kutta methods for optimal control. Zbl 1278.49037
Walther, Andrea
2007
Adjoint concepts for the optimal control of Burgers equation. Zbl 1278.49028
Noack, Antje; Walther, Andrea
2007
Maintaining factorized KKT systems subject to rank-one updates of Hessians and Jacobians. Zbl 1196.90130
Griewank, Andreas; Walther, Andrea; Korzec, Maciek
2007
Automatic differentiation of an entire design chain for aerodynamic shape optimization. Zbl 1409.76126
Gauger, Nicolas R.; Walther, Andrea; Moldenhauer, Carsten; Widhalm, Markus
2007
Application of AD-based quasi-Newton methods to stiff ODEs. Zbl 1270.65035
Schlenkrich, Sebastian; Walther, Andrea; Griewank, Andreas
2006
Towards matrix-free AD-based preconditioning of KKT systems in PDE-constrained optimization. Zbl 1391.65153
Griesse, Roland; Walther, Andrea
2005
Evaluating gradients in optimal control: continuous adjoints versus automatic differentiation. Zbl 1130.49308
Griesse, R.; Walther, A.
2004
Walther, Andrea; Griewank, Andreas
2004
Bounding the number of processors and checkpoints needed in time-minimal parallel reversal schedules. Zbl 1102.68417
Walther, A.
2004
Parametric sensitivities for optimal control problems using automatic differentiation. Zbl 1073.93518
Griesse, Roland; Walther, Andrea
2003
Walther, Andrea; Griewank, Andreas; Vogel, Olaf
2003
Introduction to automatic differentiation. Zbl 1201.68160
Griewank, Andreas; Walther, Andrea
2003
On constrained optimization by adjoint based quasi-Newton methods. Zbl 1065.90077
Griewank, Andreas; Walther, Andrea
2002
The implementation and testing of time-minimal and resource-optimal parallel reversal schedules. Zbl 1055.68526
Lehmann, U.; Walther, A.
2002
Algorithm 799: revolve: an implementation of checkpointing for the reverse or adjoint mode of computational differentiation. Zbl 1137.65330
Griewank, Andreas; Walther, Andrea
2000
Evaluating higher derivative tensors by forward propagation of univariate Taylor series. Zbl 0952.65028
Griewank, Andreas; Utke, Jean; Walther, Andrea
2000
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#### Cited by 700 Authors

 25 Walther, Andrea 17 Griewank, Andreas 8 Charpentier, Isabelle 7 Barton, Paul I. 7 Diehl, Moritz Mathias 7 Khan, Kamil A. 6 Bücker, H. Martin 6 Sandu, Adrian 5 Gauger, Nicolas R. 5 Hossain, Shahadat 5 Joshi, Mark S. 5 Lamour, René 4 Alexe, Mihai 4 Behr, Marek A. 4 Bischof, Christian H. 4 Hoppe, Ronald H. W. 4 Lehmann, Lutz 4 Müller, Jens-Dominik 4 Naumann, Uwe 4 Navon, Ionel Michael 4 Quirynen, Rien 4 Schlenkrich, Sebastian 4 Streubel, Tom 4 Wild, Stefan M. 3 Antil, Harbir 3 Asaithambi, Asai 3 Aschemann, Harald 3 Barrio, Roberto 3 Biegler, Lorenz T. 3 Bock, Hans Georg 3 Bosse, Torsten 3 Braga, Mónica 3 Cochelin, Bruno 3 Dussault, Jean-Pierre 3 Fidkowski, Krzysztof J. 3 Fiege, Sabrina 3 Gerdts, Matthias 3 Götschel, Sebastian 3 Gower, Robert Mansel 3 Gros, Sebastien 3 Hascoet, Laurent 3 Heinkenschloss, Matthias 3 Herty, Michael Matthias 3 Houska, Boris 3 Hu, Heng 3 Karasözen, Bülent 3 Kchouk, Bilel 3 Koutsawa, Yao 3 Kulshreshtha, Kshitij 3 Lukšan, Ladislav 3 Lülfesmann, Michael 3 Mäkinen, Raino A. E. 3 Marenco, Javier L. 3 Menickelly, Matt 3 Ober-Blöbaum, Sina 3 Potier-Ferry, Michel 3 Probst, Markus 3 Radons, Manuel 3 Rauh, Andreas 3 Steihaug, Trond 3 Toivanen, Jukka I. 3 Wang, Qiqi 3 Watson, Harry A. J. 3 Weiser, Martin 3 Yilmaz, Fikriye Nuray 3 Zhu, Dan 2 Abad, Alberto J. 2 Albi, Giacomo 2 Alexanderian, Alen 2 Amaran, Satyajith 2 Auer, Ekaterina 2 Aupy, Guillaume 2 Awruch, Armando Miguel 2 Banović, Mladen 2 Borgonovo, Emanuele 2 Brossier, Romain 2 Bury, Scott J. 2 Chen, Xiao 2 Christakopoulos, Faidon 2 Daya, El Mostafa 2 Degroote, Joris 2 Espath, Luis F. R. 2 Estévez Schwarz, Diana 2 Fang, Fangxin 2 Farrell, Patrick E. 2 Fiedorowicz, Anna 2 Flaßkamp, Kathrin 2 Guillot, Louis 2 Hasenfelder, Richard 2 Haslinger, Jaroslav 2 Hegerhorst-Schultchen, L. C. 2 Herrmann, Julien 2 Herzog, Roland 2 Hojny, Christopher 2 Huchette, Joey 2 Jones, Dominic 2 Kasać, Josip 2 Kusch, Lisa 2 Lampoh, Komlanvi 2 Lang, Jens ...and 600 more Authors
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#### Cited in 122 Serials

 54 Optimization Methods & Software 17 Journal of Computational and Applied Mathematics 15 Journal of Computational Physics 13 SIAM Journal on Scientific Computing 9 Computer Methods in Applied Mechanics and Engineering 9 Applied Mathematics and Computation 8 Numerical Algorithms 8 Mathematical Programming. Series A. Series B 8 SIAM Journal on Optimization 8 Computational Optimization and Applications 6 Computers and Fluids 6 Optimal Control Applications & Methods 6 Journal of Scientific Computing 5 Computers & Mathematics with Applications 5 Computer Physics Communications 5 Optimization and Engineering 4 Discrete Applied Mathematics 4 ACM Transactions on Mathematical Software 4 International Journal for Numerical Methods in Engineering 4 European Journal of Operational Research 4 Engineering Analysis with Boundary Elements 4 Computational Geosciences 4 SIAM/ASA Journal on Uncertainty Quantification 3 Computing 3 Journal of Optimization Theory and Applications 3 Mathematics and Computers in Simulation 3 Computational Mechanics 3 Applied Mathematical Modelling 3 Nonlinear Dynamics 3 Mathematics in Computer Science 3 Mathematical Programming Computation 2 International Journal of Control 2 International Journal for Numerical Methods in Fluids 2 Inverse Problems 2 Journal of Engineering Mathematics 2 Psychometrika 2 Mathematics of Computation 2 Kybernetika 2 Numerische Mathematik 2 Optimization 2 Journal of Economic Dynamics & Control 2 Journal of Global Optimization 2 Computational Statistics 2 SIAM Review 2 Discrete and Continuous Dynamical Systems 2 Journal of Combinatorial Optimization 2 International Journal of Theoretical and Applied Finance 2 Journal of Discrete Algorithms 2 Acta Numerica 2 SIAM Journal on Imaging Sciences 2 Science China. Mathematics 1 Acta Mechanica 1 Advances in Applied Probability 1 Discrete Mathematics 1 International Journal of General Systems 1 Journal of Fluid Mechanics 1 Journal of Mathematical Biology 1 Mathematical Methods in the Applied Sciences 1 Physics Reports 1 SIAM Journal on Numerical Analysis 1 Systems & Control Letters 1 Acta Applicandae Mathematicae 1 Physica D 1 Applied Numerical Mathematics 1 Graphs and Combinatorics 1 Journal of Symbolic Computation 1 Constructive Approximation 1 Algorithmica 1 Numerical Methods for Partial Differential Equations 1 Mathematical and Computer Modelling 1 Annals of Operations Research 1 Machine Learning 1 International Journal of High Speed Computing 1 International Journal of Computer Mathematics 1 Linear Algebra and its Applications 1 Computational Statistics and Data Analysis 1 Journal of Dynamics and Differential Equations 1 Journal of Mathematical Imaging and Vision 1 Journal of Nonlinear Science 1 Cybernetics and Systems Analysis 1 Advances in Applied Clifford Algebras 1 Monte Carlo Methods and Applications 1 Applied Mathematical Finance 1 INFORMS Journal on Computing 1 European Journal of Control 1 Computing and Visualization in Science 1 Mathematical Finance 1 Vietnam Journal of Mathematics 1 Soft Computing 1 Australian & New Zealand Journal of Statistics 1 Chaos 1 Mathematical and Computer Modelling of Dynamical Systems 1 International Journal of Applied Mathematics and Computer Science 1 RAIRO. Operations Research 1 Nonlinear Analysis. Modelling and Control 1 Quantitative Finance 1 Archives of Computational Methods in Engineering 1 Journal of Machine Learning Research (JMLR) 1 ASTIN Bulletin 1 Journal of Applied Mathematics and Computing ...and 22 more Serials
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#### Cited in 39 Fields

 216 Numerical analysis (65-XX) 102 Operations research, mathematical programming (90-XX) 92 Calculus of variations and optimal control; optimization (49-XX) 44 Computer science (68-XX) 39 Fluid mechanics (76-XX) 38 Partial differential equations (35-XX) 22 Ordinary differential equations (34-XX) 21 Mechanics of deformable solids (74-XX) 18 Statistics (62-XX) 17 Systems theory; control (93-XX) 15 Combinatorics (05-XX) 15 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 Probability theory and stochastic processes (60-XX) 11 Real functions (26-XX) 10 Geophysics (86-XX) 9 Biology and other natural sciences (92-XX) 8 Mechanics of particles and systems (70-XX) 6 Approximations and expansions (41-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Information and communication theory, circuits (94-XX) 4 Integral equations (45-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Operator theory (47-XX) 3 Optics, electromagnetic theory (78-XX) 3 Quantum theory (81-XX) 2 Number theory (11-XX) 2 Mathematics education (97-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistical mechanics, structure of matter (82-XX)

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