MATLAB expm swMATH ID: 14349 Software Authors: MATLAB Description: The scaling and squaring method for the matrix exponential revisited. The scaling and squaring method is the most widely used method for computing the matrix exponential, not least because it is the method implemented in the MATLAB function expm. The method scales the matrix by a power of 2 to reduce the norm to order 1, computes a Padé approximant to the matrix exponential, and then repeatedly squares to undo the effect of the scaling. ... Homepage: http://de.mathworks.com/help/matlab/ref/expm.html Dependencies: Matlab Related Software: mftoolbox; Matlab; mctoolbox; Expokit; phipm; Algorithm 919; RODAS; LAPACK; Expint; Eigtool; testmatrix; JDQZ; JDQR; Mathematica; Algorithm 432; SparseMatrix; GitHub; RKC; MPAS-Ocean; Seigtool Cited in: 179 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year The scaling and squaring method for the matrix exponential revisited. Zbl 1178.65040Higham, Nicholas J. 2009 all top 5 Cited by 315 Authors 13 Ibáñez González, Jacinto Javier 12 Higham, Nicholas J. 12 Sastre, Jorge 10 Defez, Emilio 8 Ruiz, Pedro A. 7 Nechepurenko, Yuri M. 5 Zhang, Yongtao 4 Al-Mohy, Awad H. 4 Biscay, Rolando J. 4 Sadkane, Miloud 3 Carbonell, Felix 3 de la Cruz, H. 3 Hached, Mehrez 3 Jimenez, Juan Carlos 3 Li, Dongping 3 Li, Lingfei 3 Pang, Hong-Kui 3 Sandu, Adrian 3 Sun, Haiwei 3 Tokman, Mayya 3 Xue, Jungong 3 Zhang, Gongqiu 2 Aprahamian, Mary 2 Areias, Pedro M. A. 2 Arsigny, Vincent 2 Ashi, Hala A. 2 Bader, Philipp 2 Benzi, Michele 2 Blanes, Sergio 2 Boiko, Andrey V. 2 Boito, Paola 2 Calandrini, Sara 2 Caliari, Marco 2 Cardoso, João R. 2 Chen, Shanqin 2 Cummings, Linda J. 2 Dehghan Takht Fooladi, Mehdi 2 Fasi, Massimiliano 2 Gaudreault, Stéphane 2 Gu, Chuanqing 2 Gunzburger, Max D. 2 Güttel, Stefan 2 Hashimoto, Yuka 2 Hernández, Vicente G. 2 Jbilou, Khalide 2 Kressner, Daniel 2 Lee, Spike T. 2 Lu, Dong 2 Massei, Stefano 2 Miyajima, Shinya 2 Nodera, Takashi 2 Ozaki, Tohru 2 Peinado, Jesús 2 Pennec, Xavier 2 Pudykiewicz, Janusz A. 2 Rabczuk, Timon 2 Rainwater, Greg 2 Reichel, Lothar 2 Robol, Leonardo 2 Seydaoğlu, Muaz 2 Tranquilli, Paul 2 Wu, Gang 2 Ye, Qiang 2 Zhu, Xiaojing 2 Zivcovich, Franco 1 Afanasjew, Martin 1 Akgül, Ali 1 Albanese, Claudio 1 Alexander, Carol 1 Alonso, Pedro 1 Arias, Enrique 1 Arranz Carreño, Aurelio 1 Artalejo, Jesus R. 1 Atkinson, Colin 1 Auckenthaler, T. 1 Ayache, Nicholas 1 Bader, Michael 1 Beckermann, Bernhard 1 Behnke, Ronny 1 Belyaev, Yuriĭ Nikolaevich 1 Benner, Peter 1 Bentbib, Abdeslem Hafid 1 Benth, Fred Espen 1 Bhatt, Harish P. 1 Bini, Dario Andrea 1 Birk, Carolin 1 Bocharov, Gennady A. 1 Bochev, M. A. 1 Bonet, Javier 1 Bormetti, Giacomo 1 Botev, Zdravko I. 1 Brio, Moysey 1 Callegaro, Giorgia 1 Carpentier, Justin 1 Casas, Fernando 1 Cassini, Fabio 1 Chekhovskoĭ, Igor S. 1 Cheng, Yingda 1 Chiocchetti, Simone 1 Clancy, Colm ...and 215 more Authors all top 5 Cited in 76 Serials 16 Journal of Computational Physics 14 SIAM Journal on Matrix Analysis and Applications 13 Journal of Computational and Applied Mathematics 11 Applied Mathematics and Computation 8 Linear Algebra and its Applications 7 SIAM Journal on Scientific Computing 5 Computer Methods in Applied Mechanics and Engineering 5 Applied Numerical Mathematics 3 Computers & Mathematics with Applications 3 Computer Physics Communications 3 ACM Transactions on Mathematical Software 3 SIAM Journal on Numerical Analysis 3 Mathematical and Computer Modelling 3 Numerical Algorithms 3 Advances in Computational Mathematics 2 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 2 BIT 2 Mathematics and Computers in Simulation 2 Numerische Mathematik 2 Computational Mechanics 2 Applied Mathematics Letters 2 Journal of Scientific Computing 2 Applied Mathematical Modelling 2 International Journal of Computer Mathematics 2 Numerical Linear Algebra with Applications 2 Russian Journal of Numerical Analysis and Mathematical Modelling 2 Journal of Applied Mathematics and Computing 2 SIAM Journal on Financial Mathematics 2 Journal of Applied Analysis and Computation 2 JSIAM Letters 1 Advances in Applied Probability 1 International Journal of Control 1 International Journal for Numerical Methods in Fluids 1 Journal of the Franklin Institute 1 Linear and Multilinear Algebra 1 Wave Motion 1 ZAMP. 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Simulation and Computation 1 European Journal of Operational Research 1 SIAM Review 1 Computational Statistics and Data Analysis 1 Cybernetics and Systems Analysis 1 Journal of Mathematical Sciences (New York) 1 Computational and Applied Mathematics 1 Journal of Computational Neuroscience 1 ACM Transactions on Modeling and Computer Simulation 1 Mathematical Finance 1 Multibody System Dynamics 1 Fractional Calculus & Applied Analysis 1 Far East Journal of Applied Mathematics 1 International Journal of Theoretical and Applied Finance 1 Methodology and Computing in Applied Probability 1 Discrete and Continuous Dynamical Systems. Series B 1 Portugaliae Mathematica. Nova Série 1 Journal of Numerical Mathematics 1 International Journal of Numerical Analysis and Modeling 1 Journal of Computational Acoustics 1 Journal of Biological Dynamics 1 Optimization Letters 1 SIAM Journal on Imaging Sciences 1 Discrete and Continuous Dynamical Systems. Series S 1 International Journal of Numerical Methods and Applications 1 Computational Methods for Differential Equations 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys all top 5 Cited in 30 Fields 146 Numerical analysis (65-XX) 49 Linear and multilinear algebra; matrix theory (15-XX) 28 Ordinary differential equations (34-XX) 19 Partial differential equations (35-XX) 19 Probability theory and stochastic processes (60-XX) 12 Fluid mechanics (76-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Biology and other natural sciences (92-XX) 7 Mechanics of deformable solids (74-XX) 6 Approximations and expansions (41-XX) 6 Quantum theory (81-XX) 5 Operations research, mathematical programming (90-XX) 4 Combinatorics (05-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Geophysics (86-XX) 3 Topological groups, Lie groups (22-XX) 3 Real functions (26-XX) 3 Differential geometry (53-XX) 3 Statistics (62-XX) 3 Optics, electromagnetic theory (78-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Special functions (33-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Mechanics of particles and systems (70-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Integral transforms, operational calculus (44-XX) 1 Operator theory (47-XX) 1 Computer science (68-XX) Citations by Year