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; RODES; Mathematica; MPFR; GitHub; Chebfun; galepu; kv; CkAnalytic; Cosy; filib++; LAPACK Cited in: 495 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year INTLAB – INTerval LABoratory. Zbl 0949.65046Rump, Siegfried M. 1999 all top 5 Cited by 533 Authors 38 Rump, Siegfried Michael 37 Lessard, Jean-Philippe 29 Miyajima, Shinya 28 Nakao, Mitsuhiro T. 28 Oishi, Shin’ichi 18 Mireles-James, Jason D. 17 Watanabe, Yoshitaka 15 van den Berg, Jan Bouwe 14 Ogita, Takeshi 13 Kinoshita, Takehiko 12 Hladík, Milan 11 Takayasu, Akitoshi 10 Castelli, Roberto 10 Liu, Xuefeng 10 Tanaka, Kazuaki 9 Kimura, Takuma 9 Monsi, Mansor Bin 9 Neumaier, Arnold 8 Breden, Maxime 8 Frommer, Andreas 8 Plum, Michael 8 Wanner, Thomas 7 Hashemi, Behnam 7 Hashimoto, Kouji 7 Mizuguchi, Makoto 7 Wang, Zhengyu 7 Yamamoto, Nobito 6 Eichfelder, Gabriele 6 Hassan, Nasruddin 6 Nataraj, Paluri S. V. 6 Ozaki, Katsuhisa 6 Ryoo, Cheon Seoung 6 Sekine, Kouta 5 Alefeld, Götz E. 5 Antil, Harbir 5 Csendes, Tibor 5 Dehghani-Madiseh, Marzieh 5 Goldsztejn, Alexandre 5 Hoppe, Ronald H. W. 5 Jaquette, Jonathan 5 Kearfott, Baker 5 Kolev, Lubomir V. 5 Li, Zhe 5 Minamoto, Teruya 5 Rauh, Andreas 5 Schichl, Hermann 4 Chen, Xiaojun 4 Church, Kevin E. M. 4 Dehghan Takht Fooladi, Mehdi 4 Domes, Ferenc 4 Heinkenschloss, Matthias 4 Leong, Wah June 4 Nagatou, Kaori 4 Revol, Nathalie 4 Stein, Oliver 4 Toyonaga, Kenji 3 Aschemann, Harald 3 Auer, Ekaterina 3 Barker, Blake 3 Chen, Yangquan 3 Corliss, George F. 3 Eftekhari, Tahereh 3 García-Azpeitia, Carlos 3 Hassan, Malik Abu 3 Hofer, Eberhard P. 3 Kepley, Shane 3 Krämer, Walter 3 Lamour, René 3 Lang, Bruno 3 Linsenmann, Christopher 3 Luther, Wolfram Jérôme 3 Markov, Svetoslav Marinovich 3 Martins, Samir Angelo Milani 3 Matsue, Kaname 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 3 Zhi, Lihong 2 Adjiman, Claire S. 2 Ahn, Hyo-Sung 2 Alt, René 2 Arounassalame, M. 2 Asai, Taisei 2 Bakar, Norhaliza Abu 2 Bakhtiari, Parisa 2 Bünger, Florian 2 Cai, Shuting 2 Capinski, Maciej J. 2 Cuyt, Annie A. M. 2 Estévez Schwarz, Diana 2 Fogelklou, Oswald ...and 433 more Authors all top 5 Cited in 138 Serials 54 Journal of Computational and Applied Mathematics 24 Japan Journal of Industrial and Applied Mathematics 19 Applied Mathematics and Computation 18 Journal of Global Optimization 15 Linear Algebra and its Applications 15 Reliable Computing 13 Journal of Differential Equations 12 SIAM Journal on Applied Dynamical Systems 11 BIT 11 Numerical Algorithms 10 Computing 10 SIAM Journal on Numerical Analysis 8 ACM Transactions on Mathematical Software 8 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 Nonlinearity 5 Automatica 4 Numerical Functional Analysis and Optimization 4 Numerische Mathematik 4 Applied Numerical Mathematics 4 Journal of Dynamics and Differential Equations 4 Indagationes Mathematicae. New Series 4 SIAM Journal on Scientific Computing 4 Foundations of Computational Mathematics 3 Journal of Mathematical Analysis and Applications 3 Calcolo 3 International Journal for Numerical Methods in Engineering 3 Physica D 3 Mathematical Programming. Series A. Series B 3 Celestial Mechanics and Dynamical Astronomy 3 SIAM Journal on Optimization 3 Journal of Nonlinear Science 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 Journal of Systems Science and Complexity 2 Archive for Rational Mechanics and Analysis 2 Journal of Computational Physics 2 Mathematics of Computation 2 Information Sciences 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Mathematical and Computer Modelling 2 Journal of Scientific Computing 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 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 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 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 Opsearch 1 Revista de la Unión Matemática Argentina 1 Theoretical Computer Science 1 Mathematica Numerica Sinica 1 Acta Applicandae Mathematicae 1 Optimization 1 Journal of Complexity 1 Constructive Approximation 1 IMA Journal of Mathematical Control and Information 1 COMPEL 1 Applied Mathematics Letters 1 European Journal of Applied Mathematics 1 The Annals of Applied Probability 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 ...and 38 more Serials all top 5 Cited in 44 Fields 374 Numerical analysis (65-XX) 90 Partial differential equations (35-XX) 64 Linear and multilinear algebra; matrix theory (15-XX) 62 Operations research, mathematical programming (90-XX) 54 Ordinary differential equations (34-XX) 43 Dynamical systems and ergodic theory (37-XX) 39 Computer science (68-XX) 26 Systems theory; control (93-XX) 25 Operator theory (47-XX) 18 Fluid mechanics (76-XX) 14 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) 10 Mechanics of deformable solids (74-XX) 9 Approximations and expansions (41-XX) 8 Probability theory and stochastic processes (60-XX) 7 Commutative algebra (13-XX) 7 Biology and other natural sciences (92-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 Special functions (33-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Functional analysis (46-XX) 3 Mathematical logic and foundations (03-XX) 3 Combinatorics (05-XX) 3 Algebraic geometry (14-XX) 3 Statistics (62-XX) 3 Optics, electromagnetic theory (78-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 General and overarching topics; collections (00-XX) 2 Number theory (11-XX) 2 Difference and functional equations (39-XX) 2 Integral equations (45-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) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year