## INTLAB

 swMATH ID: 4004 Software Authors: Rump, Siegfried M. Description: INTLAB is the Matlab toolbox for reliable computing and self-validating algorithms. It comprises of self-validating methods for dense linear systems (also inner inclusions and structured matrices) sparse s.p.d. linear systems systems of nonlinear equations (including unconstrained optimization) roots of univariate and multivariate nonlinear equations (simple and clusters) eigenvalue problems (simple and clusters, also inner inclusions and structured matrices) generalized eigenvalue problems (simple and clusters) quadrature for univariate functions univariate polynomial zeros (simple and clusters) interval arithmetic for real and complex data including vectors and matrices (very fast) interval arithmetic for real and complex sparse matrices (very fast) automatic differentiation (forward mode, vectorized computations, fast) Gradients (to solve systems of nonlinear equations) Hessians (for global optimization) Taylor series for univariate functions automatic slopes (sequential approach, slow for many variables) verified integration of (simple) univariate functions univariate and multivariate (interval) polynomials rigorous real interval standard functions (fast, very accurate,  3 ulps) rigorous complex interval standard functions (fast, rigorous, but not necessarily sharp inclusions) rigorous input/output (outer and inner inclusions) accurate summation, dot product and matrix-vector residuals (interpreted, reference implementation, slow) multiple precision interval arithmetic with error bounds (does the job, slow) Homepage: http://www.ti3.tu-harburg.de/rump/intlab/ Dependencies: Matlab Related Software: Matlab; mctoolbox; C-XSC 2.0; C-XSC; INTOPT_90; VERSOFT; PROFIL/BIAS; mftoolbox; BLAS; Mathematica; MPFR; galepu; RODES; CkAnalytic; Cosy; filib++; LAPACK; GitHub; Chebfun; kv Referenced in: 470 Publications

### Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
INTLAB – INTerval LABoratory. Zbl 0949.65046
Rump, Siegfried M.
1999
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### Referenced by 498 Authors

 35 Lessard, Jean-Philippe 34 Rump, Siegfried Michael 28 Miyajima, Shinya 27 Oishi, Shin’ichi 24 Nakao, Mitsuhiro T. 17 Mireles-James, Jason D. 15 van den Berg, Jan Bouwe 15 Watanabe, Yoshitaka 14 Ogita, Takeshi 12 Hladík, Milan 10 Castelli, Roberto 10 Kinoshita, Takehiko 10 Tanaka, Kazuaki 9 Liu, Xuefeng 9 Monsi, Mansor Bin 9 Neumaier, Arnold 8 Frommer, Andreas 8 Plum, Michael 8 Takayasu, Akitoshi 8 Wanner, Thomas 7 Breden, Maxime 7 Hashemi, Behnam 7 Kimura, Takuma 6 Eichfelder, Gabriele 6 Hashimoto, Kouji 6 Hassan, Nasruddin 6 Mizuguchi, Makoto 6 Nataraj, Paluri S. V. 6 Ozaki, Katsuhisa 6 Ryoo, Cheon Seoung 6 Yamamoto, Nobito 5 Alefeld, Götz E. 5 Antil, Harbir 5 Csendes, Tibor 5 Goldsztejn, Alexandre 5 Hoppe, Ronald H. W. 5 Kearfott, Baker 5 Kolev, Lubomir V. 5 Li, Zhe 5 Rauh, Andreas 5 Schichl, Hermann 5 Sekine, Kouta 4 Chen, Xiaojun 4 Church, Kevin E. M. 4 Dehghan Takht Fooladi, Mehdi 4 Dehghani-Madiseh, Marzieh 4 Domes, Ferenc 4 Heinkenschloss, Matthias 4 Jaquette, Jonathan 4 Minamoto, Teruya 4 Nagatou, Kaori 4 Revol, Nathalie 4 Stein, Oliver 4 Toyonaga, Kenji 4 Wang, Zhengyu 3 Aschemann, Harald 3 Auer, Ekaterina 3 Chen, Yangquan 3 Corliss, George F. 3 Eftekhari, Tahereh 3 García-Azpeitia, Carlos 3 Hofer, Eberhard P. 3 Krämer, Walter 3 Lamour, René 3 Lang, Bruno 3 Leong, Wah June 3 Linsenmann, Christopher 3 Luther, Wolfram Jérôme 3 Martins, Samir A. M. 3 Mischaikow, Konstantin 3 Neher, Markus 3 Nepomuceno, Erivelton Geraldo 3 Niebling, Julia 3 Rodrigues, Heitor M. Junior 3 Sakurai, Tetsuya 3 Sander, Evelyn 3 Sugiura, Hiroshi 3 Tucker, Warwick 3 Walter, Eric 3 Xia, Bican 3 You, Chunguang 2 Adjiman, Claire S. 2 Ahn, Hyo-Sung 2 Alt, René 2 Arounassalame, M. 2 Asai, Taisei 2 Bakhtiari, Parisa 2 Barker, Blake 2 Bünger, Florian 2 Cai, Shuting 2 Cuyt, Annie A. M. 2 Estévez Schwarz, Diana 2 Fogelklou, Oswald 2 Gameiro, Marcio F. 2 Garloff, Jürgen 2 Glomski, Matthew 2 Jamaludin, Noraini 2 Jansson, Christian 2 Jaulin, Luc 2 Kepley, Shane ...and 398 more Authors
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### Referenced in 132 Serials

 52 Journal of Computational and Applied Mathematics 22 Japan Journal of Industrial and Applied Mathematics 19 Applied Mathematics and Computation 18 Journal of Global Optimization 15 Reliable Computing 14 Linear Algebra and its Applications 12 Journal of Differential Equations 12 SIAM Journal on Applied Dynamical Systems 11 Numerical Algorithms 10 BIT 10 Computing 10 SIAM Journal on Numerical Analysis 8 ACM Transactions on Mathematical Software 7 SIAM Journal on Matrix Analysis and Applications 6 Numerical Linear Algebra with Applications 6 Soft Computing 6 Communications in Nonlinear Science and Numerical Simulation 6 Applied Mathematical Sciences (Ruse) 6 Journal of Computational Dynamics 5 Computers & Mathematics with Applications 5 Automatica 4 Nonlinearity 4 Numerical Functional Analysis and Optimization 4 Applied Numerical Mathematics 4 Journal of Dynamics and Differential Equations 4 Indagationes Mathematicae. New Series 4 SIAM Journal on Scientific Computing 3 Journal of Mathematical Analysis and Applications 3 International Journal for Numerical Methods in Engineering 3 Numerische Mathematik 3 Physica D 3 Mathematical Programming. Series A. Series B 3 Celestial Mechanics and Dynamical Astronomy 3 SIAM Journal on Optimization 3 Computational and Applied Mathematics 3 ELA. The Electronic Journal of Linear Algebra 3 Optimization Methods & Software 3 International Journal of Applied Mathematics and Computer Science 3 Foundations of Computational Mathematics 2 Journal of Computational Physics 2 Mathematics of Computation 2 Calcolo 2 Information Sciences 2 Mathematical and Computer Modelling 2 Applications of Mathematics 2 SIAM Journal on Mathematical Analysis 2 International Journal of Robust and Nonlinear Control 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Journal of Nonlinear Science 2 Advances in Computational Mathematics 2 Discrete and Continuous Dynamical Systems 2 Journal of Inequalities and Applications 2 Far East Journal of Mathematical Sciences 2 Discrete and Continuous Dynamical Systems. Series B 2 Journal of Systems Science and Complexity 2 Journal of Machine Learning Research (JMLR) 2 International Journal of Pure and Applied Mathematics 2 Mathematics in Computer Science 2 International Journal of Mathematical Analysis (Ruse) 1 Artificial Intelligence 1 Archive for Rational Mechanics and Analysis 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Engineering Mathematics 1 Journal of the Franklin Institute 1 Linear and Multilinear Algebra 1 Advances in Mathematics 1 Control and Cybernetics 1 Czechoslovak Mathematical Journal 1 Integral Equations and Operator Theory 1 International Journal of Circuit Theory and Applications 1 Journal of Optimization Theory and Applications 1 Mathematics and Computers in Simulation 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Opsearch 1 Revista de la Unión Matemática Argentina 1 Theoretical Computer Science 1 Acta Applicandae Mathematicae 1 Journal of Complexity 1 Constructive Approximation 1 IMA Journal of Mathematical Control and Information 1 COMPEL 1 Applied Mathematics Letters 1 Journal of Scientific Computing 1 European Journal of Applied Mathematics 1 Computational Geometry 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Computational Statistics 1 Alkalmazott Matematikai Lapok. A Magyar Tudomanyos Akademia. Matematikai es Fizikai Tudomanyok Osztalyanak Közlemenyei 1 Applied Mathematical Modelling 1 International Journal of Computer Mathematics 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Formal Methods in System Design 1 Turkish Journal of Mathematics 1 NoDEA. Nonlinear Differential Equations and Applications 1 Selecta Mathematica. New Series 1 Journal of Geodesy 1 Mathematical Problems in Engineering 1 Computing and Visualization in Science 1 Vychislitel’nye Tekhnologii 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik ...and 32 more Serials
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### Referenced in 43 Fields

 359 Numerical analysis (65-XX) 83 Partial differential equations (35-XX) 61 Linear and multilinear algebra; matrix theory (15-XX) 58 Operations research, mathematical programming (90-XX) 51 Ordinary differential equations (34-XX) 41 Dynamical systems and ergodic theory (37-XX) 37 Computer science (68-XX) 26 Systems theory; control (93-XX) 22 Operator theory (47-XX) 17 Fluid mechanics (76-XX) 13 Mechanics of particles and systems (70-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 10 Functions of a complex variable (30-XX) 9 Mechanics of deformable solids (74-XX) 8 Approximations and expansions (41-XX) 7 Probability theory and stochastic processes (60-XX) 7 Biology and other natural sciences (92-XX) 6 Commutative algebra (13-XX) 6 Real functions (26-XX) 5 Field theory and polynomials (12-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Information and communication theory, circuits (94-XX) 4 Functional analysis (46-XX) 3 Mathematical logic and foundations (03-XX) 3 Combinatorics (05-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Statistics (62-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 General and overarching topics; collections (00-XX) 2 Number theory (11-XX) 2 Algebraic geometry (14-XX) 2 Special functions (33-XX) 2 Difference and functional equations (39-XX) 2 Integral equations (45-XX) 2 Optics, electromagnetic theory (78-XX) 1 Measure and integration (28-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Quantum theory (81-XX) 1 Geophysics (86-XX)