## NewtonLib

 swMATH ID: 4796 Software Authors: Deuflhard, Peter; Lutz Weimann Description: Numerical Mathematics - NewtonLib. Software repository for Peter Deuflhards Book ”Newton Methods for Nonlinear Problems – Affine Invariance and Adaptive Algorithms”. This monograph presents a scheme to construct adaptive Newton-type algorithms in close connection with an associated affine invariant convergence analysis. Part of these algorithms are presented as informal programs in the text. Some, but not all of the described algorithms have been worked out in detail. Below follows a list of codes mentioned by name in the book. All of the available programs (not only by the author and his group) are free as long as they are exclusively used for research or teaching purposes. For commercial use of the software you must sign a license-agreement with the ZIB and pay a license-charge that depends on the referenced software package and the intended usage. Please read our sample license agreement (or the german version) for more details. Homepage: http://www.zib.de/weimann/NewtonLib/index.html Keywords: Newton method; nonlinear problems; affine invariance; adaptive algorithms; textbook; convergence; Banach spaces; affine covariance; affine contravariance; affine conjugacy; affine similarity; error norms; residual norms; energy norms; steepest descent methods; trust region methods; Levenberg Marquardt methods; Gauss-Newton methods; nonlinear least squares; stiff initial value problems; Picard iteration; multilevel collocation method; finite element methods; numerical examples Related Software: Matlab; RODAS; PETSc; KELLEY; DUNE; ALCON; Ipopt; minpack; PARDISO; MATLAB ODE suite; ode23s; ode113; Ode15s; ode45; ode23; SOCS; FEniCS; mctoolbox; IPARS; Bertini Cited in: 314 Publications
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### Cited by 499 Authors

 29 Argyros, Ioannis Konstantinos 20 Hilout, Saïd 13 Deuflhard, Peter 12 Hoppe, Ronald H. W. 8 Linsenmann, Christopher 8 Schiela, Anton 8 Tchelepi, Hamdi A. 8 Weiser, Martin 7 Hamon, François P. 6 Antil, Harbir 6 Potschka, Andreas 5 Augustin, Christoph M. 5 Liu, Wen-Jie 5 Luo, Xinlong 5 Sun, Jiebao 5 Volkwein, Stefan 5 Wohlmuth, Barbara I. 5 Wu, Boying 4 Diehl, Moritz Mathias 4 Liu, Chein-Shan 4 Pavarino, Luca Franco 4 Plank, Gernot 4 Wu, Shulin 3 Atluri, Satya N. 3 Ferreira, Orizon Pereira 3 Gsell, Matthias A. F. 3 Hager, Corinna 3 Horenko, Illia 3 Karabelas, Elias 3 Kelley, Carl T. 3 Lass, Oliver 3 Lemoine, Jérôme 3 Mallison, Bradley T. 3 Münch, Arnaud 3 Munteanu, Marilena 3 Polyak, Boris Teodorovich 3 Quirynen, Rien 3 Tran Dinh Quoc 2 Adler, James H. 2 Amat, Sergio P. 2 Bebendorf, Mario 2 Bertolazzi, Enrico 2 Beyn, Wolf-Jürgen 2 Bock, Hans Georg 2 Bonnans, Joseph Frédéric 2 Busquier, Sonia 2 Caboussat, Alexandre 2 Cho, Yeol Je 2 Descombes, Stéphane 2 Duarte, Max 2 Erdmann, Bodo 2 Gänzler, Tobias 2 Geiser, Jürgen 2 Glowinski, Roland 2 Götschel, Sebastian 2 Gros, Sebastien 2 Haase, Gundolf 2 Huang, Chengming 2 Jarlebring, Elias 2 Jiang, Jiamin 2 Kokurin, Mikhail Yur’evich 2 Krause, Rolf H. 2 Kressner, Daniel 2 Kunkel, Peter 2 Landry, Chantal 2 Leykin, Anton 2 Li, Dongfang 2 Li, Xiaolin 2 Ling, Yonghui 2 Magreñán, Ángel Alberto 2 Martinon, Pierre 2 Massot, Marc 2 Mehrmann, Volker 2 Petrova, Svetozara I. 2 Pulch, Roland 2 Ramos, Higinio 2 Ren, Hongmin 2 Röblitz, Susanna 2 Schöps, Sebastian 2 Schulz, Volker H. 2 Schütte, Christof 2 Shamanskiy, Alexander 2 Simeon, Bernd 2 Stöcklein, Matthias 2 Stötzel, Claudia 2 Tchoń, Krzysztof 2 Ulbrich, Stefan 2 Verschelde, Jan 2 Vohralík, Martin 2 Wheeler, Mary Fanett 2 Xiao, Hang 2 Xu, Xiubin 2 Zhao, Ailing 2 Zhou, Tao 2 Zhu, Jialin 1 Abdulle, Assyr 1 Absil, Pierre-Antoine 1 Ackermann, Wolfgang 1 Agarwal, Ravi P. 1 Aidi, Khaoula ...and 399 more Authors
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### Cited in 114 Serials

 18 SIAM Journal on Scientific Computing 15 Computer Methods in Applied Mechanics and Engineering 15 Journal of Computational Physics 15 Journal of Computational and Applied Mathematics 14 SIAM Journal on Numerical Analysis 13 Applied Mathematics and Computation 10 Numerical Algorithms 7 Optimization Methods & Software 6 Journal of Optimization Theory and Applications 6 Numerische Mathematik 6 Applied Numerical Mathematics 6 SIAM Journal on Optimization 5 Computational Optimization and Applications 4 Computers & Mathematics with Applications 4 Journal of Mathematical Analysis and Applications 4 Journal of Complexity 4 Journal of Scientific Computing 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Computational Geosciences 4 Journal of Theoretical Biology 3 Mathematical Methods in the Applied Sciences 3 Mathematics and Computers in Simulation 3 SIAM Journal on Control and Optimization 3 Computational Mechanics 3 Applied Mathematical Modelling 3 International Journal of Computer Mathematics 3 Mathematical Programming. Series A. Series B 3 Applicationes Mathematicae 3 Advances in Computational Mathematics 3 Mathematical and Computer Modelling of Dynamical Systems 3 CMES. Computer Modeling in Engineering & Sciences 3 Journal of Numerical Mathematics 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Springer Series in Computational Mathematics 2 Computing 2 International Journal for Numerical Methods in Engineering 2 Journal of Computational Mathematics 2 Vietnam Journal of Mathematics 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Foundations of Computational Mathematics 2 Journal of Applied Mathematics and Computing 2 Multiscale Modeling & Simulation 2 Acta Numerica 2 Texts in Applied Mathematics 1 Classical and Quantum Gravity 1 IMA Journal of Numerical Analysis 1 International Journal of Control 1 International Journal for Numerical Methods in Fluids 1 Inverse Problems 1 Journal of Engineering Mathematics 1 Journal of Fluid Mechanics 1 Mathematics of Computation 1 Bulletin of Mathematical Biology 1 Automatica 1 BIT 1 Control and Cybernetics 1 Czechoslovak Mathematical Journal 1 Mathematics of Operations Research 1 Numerical Functional Analysis and Optimization 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Theoretical Computer Science 1 Systems & Control Letters 1 Applied Mathematics and Mechanics. (English Edition) 1 Physica D 1 Journal of Symbolic Computation 1 Numerical Methods for Partial Differential Equations 1 SIAM Journal on Matrix Analysis and Applications 1 Signal Processing 1 Journal of Global Optimization 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Computational Statistics 1 Aequationes Mathematicae 1 Elemente der Mathematik 1 European Journal of Operational Research 1 Journal of Statistical Computation and Simulation 1 Linear Algebra and its Applications 1 SIAM Journal on Applied Mathematics 1 SIAM Review 1 Journal of Nonlinear Science 1 Advances in Engineering Software 1 Journal of Mathematical Sciences (New York) 1 Computational and Applied Mathematics 1 Fractals 1 Journal of Inverse and Ill-Posed Problems 1 Statistica Sinica 1 Engineering Analysis with Boundary Elements 1 Documenta Mathematica 1 Science in China. Series E 1 Journal of Mathematical Chemistry 1 Mathematical Problems in Engineering 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Multibody System Dynamics 1 Journal of Inequalities and Applications 1 Journal of Mathematical Fluid Mechanics 1 Optimization and Engineering 1 SIAM Journal on Applied Dynamical Systems 1 Analysis and Applications (Singapore) 1 International Journal of Numerical Analysis and Modeling 1 Cubo 1 Oberwolfach Reports ...and 14 more Serials
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### Cited in 39 Fields

 229 Numerical analysis (65-XX) 56 Partial differential equations (35-XX) 54 Calculus of variations and optimal control; optimization (49-XX) 43 Operations research, mathematical programming (90-XX) 40 Fluid mechanics (76-XX) 39 Operator theory (47-XX) 30 Mechanics of deformable solids (74-XX) 27 Ordinary differential equations (34-XX) 24 Biology and other natural sciences (92-XX) 11 Optics, electromagnetic theory (78-XX) 10 Dynamical systems and ergodic theory (37-XX) 8 Integral equations (45-XX) 8 Statistics (62-XX) 8 Systems theory; control (93-XX) 7 Mechanics of particles and systems (70-XX) 6 Global analysis, analysis on manifolds (58-XX) 6 Probability theory and stochastic processes (60-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Classical thermodynamics, heat transfer (80-XX) 5 Geophysics (86-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Field theory and polynomials (12-XX) 3 Functions of a complex variable (30-XX) 3 Information and communication theory, circuits (94-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Real functions (26-XX) 2 Difference and functional equations (39-XX) 2 Approximations and expansions (41-XX) 2 Functional analysis (46-XX) 2 Computer science (68-XX) 2 Mathematics education (97-XX) 1 Algebraic geometry (14-XX) 1 Sequences, series, summability (40-XX) 1 Differential geometry (53-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)