swMATH ID: 23743
Software Authors: N. J. Higham
Description: The Matrix Function Toolbox is a MATLAB toolbox connected with functions of matrices. It is associated with the book Functions of Matrices: Theory and Computation and contains implementations of many of the algorithms described in the book. The book is the main documentation for the toolbox. The toolbox is intended to facilitate understanding of the algorithms through MATLAB experiments, to be useful for research in the subject, and to provide a basis for the development of more sophisticated implementations. The codes are ”plain vanilla” versions; they contain the core algorithmic aspects with a minimum of inessential code. In particular, the following features should be noted. The codes have little error checking of input arguments. The codes do not print intermediate results or the progress of an iteration. For the iterative algorithms a convergence tolerance is hard-coded (in function mft_tolerance). For greater flexibility this tolerance could be made an input argument. The codes are designed for simplicity and readability rather than maximum efficiency. Algorithmic options such as preprocessing are omitted. The codes are intended for double precision matrices. Those algorithms in which the parameters can be adapted to the precision have not been written to take advantage of single precision inputs.
Homepage: http://www.maths.manchester.ac.uk/~higham/mftoolbox/
Related Software: mctoolbox; Matlab; MATLAB expm; Expokit; SparseMatrix; Eigtool; INTLAB; phipm; Algorithm 919; blgaussexp; testmatrix; OPQ; Algorithm 432; Mathematica; LAPACK; Chebfun; RODAS; sgcen; JDQZ; Matrix Means Toolbox
Cited in: 637 Publications

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Functions of matrices. Theory and computation. Zbl 1167.15001
Higham, Nicholas J.
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Cited by 880 Authors

16 Higham, Nicholas J.
16 Ibáñez González, Jacinto Javier
16 Miyajima, Shinya
16 Reichel, Lothar
16 Sastre, Jorge
15 Defez, Emilio
15 Soleymani, Fazlollah
14 Vabishchevich, Pëtr Nikolaevich
12 Benzi, Michele
12 Nakatsukasa, Yuji
10 Iannazzo, Bruno
9 Noferini, Vanni
8 Bini, Dario Andrea
8 Estrada, Ernesto
8 Frommer, Andreas
8 Gawlik, Evan S.
7 Benner, Peter
7 Cardoso, João R.
7 Meini, Beatrice
7 Peinado, Jesús
7 Ruiz, Pedro A.
7 Simoncini, Valeria
6 Al-Mohy, Awad H.
6 Arrigo, Francesca
6 Guo, Chun-Hua
6 Kressner, Daniel
6 Massei, Stefano
6 Novati, Paolo
6 Ziętak, Krystyna
5 Abdalla, Mohamed
5 Beckermann, Bernhard
5 Bochev, M. A.
5 Fasi, Massimiliano
5 Güttel, Stefan
5 Jagels, Carl F.
5 Kürschner, Patrick
5 Leok, Melvin
5 Mitrouli, Marilena
5 Neff, Patrizio
5 Pozza, Stefano
5 Robol, Leonardo
5 Schweitzer, Marcel
5 Shateyi, Stanford
5 Wu, Gang
4 Brezinski, Claude
4 De la Cruz Cabrera, Omar
4 Dehghan Takht Fooladi, Mehdi
4 Del Moral, Pierre
4 Durastante, Fabio
4 Fika, Paraskevi
4 Jbilou, Khalide
4 Kurbatov, Vitaliĭ Gennad’evich
4 Kurbatova, Irina Vital’evna
4 Latouche, Guy
4 Li, Dongping
4 Lyu, Shulin
4 Maset, Stefano
4 Poloni, Federico G.
4 Redivo-Zaglia, Michela
4 Relton, Samuel D.
4 Sadeghi, Amir
4 Sun, Haiwei
4 Tisseur, Françoise
4 Zhu, Xiaojing
3 Acebrón, Juan A.
3 Aceto, Lidia
3 Alonso-Jordá, Pedro
3 Alonso, Pedro
3 Alqahtani, Hessah
3 Auzinger, Winfried
3 Baake, Michael
3 Bishop, Adrian N.
3 Boito, Paola
3 Bolsinov, Alexey V.
3 Chen, Yang
3 Deadman, Edvin
3 Greco, Federico
3 Hackbusch, Wolfgang
3 Ju, Lili
3 Khaksar Haghani, F.
3 Li, Xiao
3 Lotfi, Taher
3 Lu, Di
3 Martin, Robert J.
3 Matveev, Vladimir S.
3 Mehrmann, Volker
3 Noschese, Silvia
3 Popolizio, Marina
3 Pranic, Miroslav S.
3 Saak, Jens
3 Schnörr, Christoph
3 Sogabe, Tomohiro
3 Stanimirović, Predrag S.
3 Toutounian, Faezeh
3 Wei, Yimin
3 Zhang, Lu
2 Abd-Elmageed, Hala
2 Abul-ez, M. A.
2 Akgül, Ali
2 Al Mugahwi, Mohammed
...and 780 more Authors
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Cited in 190 Serials

71 Linear Algebra and its Applications
41 SIAM Journal on Matrix Analysis and Applications
40 Journal of Computational and Applied Mathematics
30 Numerical Algorithms
22 Applied Mathematics and Computation
21 SIAM Journal on Scientific Computing
19 BIT
14 Applied Numerical Mathematics
12 Numerische Mathematik
11 Journal of Computational Physics
11 Journal of Scientific Computing
10 Numerical Linear Algebra with Applications
9 Journal of Mathematical Analysis and Applications
9 Calcolo
7 Computers & Mathematics with Applications
7 Computational and Applied Mathematics
7 ELA. The Electronic Journal of Linear Algebra
6 Computer Physics Communications
6 Journal of the Franklin Institute
6 Foundations of Computational Mathematics
5 Mathematics and Computers in Simulation
5 Systems & Control Letters
5 Applied Mathematics Letters
5 SIAM Review
5 ETNA. Electronic Transactions on Numerical Analysis
5 Advances in Computational Mathematics
5 Fractional Calculus & Applied Analysis
4 Journal of Mathematical Physics
4 Linear and Multilinear Algebra
4 Automatica
4 SIAM Journal on Numerical Analysis
4 Mathematical and Computer Modelling
4 Applied Mathematical Modelling
4 Computational Methods in Applied Mathematics
3 Inverse Problems
3 Japan Journal of Industrial and Applied Mathematics
3 Abstract and Applied Analysis
3 Discrete and Continuous Dynamical Systems. Series B
3 Acta Numerica
3 Communications in Computational Physics
3 Statistics and Computing
3 Journal of Theoretical Biology
3 JSIAM Letters
3 Journal of Linear and Topological Algebra
3 Journal of Function Spaces
2 Advances in Applied Probability
2 Discrete Applied Mathematics
2 Wave Motion
2 ZAMP. Zeitschrift für angewandte Mathematik und Physik
2 Mathematics of Computation
2 Transactions of the American Mathematical Society
2 Constructive Approximation
2 Computational Mechanics
2 Neural Computation
2 Computational Mathematics and Mathematical Physics
2 SIAM Journal on Applied Mathematics
2 SIAM Journal on Optimization
2 Journal of Mathematical Imaging and Vision
2 Computational Optimization and Applications
2 Electronic Journal of Differential Equations (EJDE)
2 Journal of the Egyptian Mathematical Society
2 Advances in Applied Clifford Algebras
2 Vietnam Journal of Mathematics
2 Mathematical Inequalities & Applications
2 Journal of Applied Mathematics
2 SIAM Journal on Imaging Sciences
2 Discrete and Continuous Dynamical Systems. Series S
2 S\(\vec{\text{e}}\)MA Journal
2 SIAM/ASA Journal on Uncertainty Quantification
2 Special Matrices
2 Journal of Mathematical Modeling
2 Computational Methods for Differential Equations
2 Advances in Operator Theory
1 Archive for Rational Mechanics and Analysis
1 Classical and Quantum Gravity
1 Computers and Fluids
1 Communications in Mathematical Physics
1 Computer Methods in Applied Mechanics and Engineering
1 Discrete Mathematics
1 International Journal of Control
1 International Journal of Engineering Science
1 Journal of Mathematical Biology
1 Mathematical Methods in the Applied Sciences
1 Nuclear Physics. B
1 Bulletin of Mathematical Biology
1 Chaos, Solitons and Fractals
1 ACM Transactions on Mathematical Software
1 Advances in Mathematics
1 The Annals of Probability
1 Demonstratio Mathematica
1 Integral Equations and Operator Theory
1 Journal of Algebra
1 Journal of Approximation Theory
1 Journal of Econometrics
1 Journal of Multivariate Analysis
1 Journal of Optimization Theory and Applications
1 Mathematica Slovaca
1 Proceedings of the American Mathematical Society
1 Rendiconti dell’Istituto di Matematica dell’Università di Trieste
1 Results in Mathematics
...and 90 more Serials
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Cited in 55 Fields

431 Numerical analysis (65-XX)
291 Linear and multilinear algebra; matrix theory (15-XX)
65 Partial differential equations (35-XX)
39 Ordinary differential equations (34-XX)
37 Combinatorics (05-XX)
35 Operator theory (47-XX)
35 Systems theory; control (93-XX)
32 Probability theory and stochastic processes (60-XX)
30 Statistics (62-XX)
24 Approximations and expansions (41-XX)
23 Real functions (26-XX)
21 Operations research, mathematical programming (90-XX)
17 Special functions (33-XX)
17 Differential geometry (53-XX)
17 Computer science (68-XX)
16 Quantum theory (81-XX)
13 Calculus of variations and optimal control; optimization (49-XX)
12 Mechanics of deformable solids (74-XX)
12 Fluid mechanics (76-XX)
11 Dynamical systems and ergodic theory (37-XX)
10 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
10 Biology and other natural sciences (92-XX)
10 Information and communication theory, circuits (94-XX)
9 Mechanics of particles and systems (70-XX)
8 Difference and functional equations (39-XX)
7 Associative rings and algebras (16-XX)
6 Functions of a complex variable (30-XX)
5 Harmonic analysis on Euclidean spaces (42-XX)
5 Functional analysis (46-XX)
5 Statistical mechanics, structure of matter (82-XX)
4 Number theory (11-XX)
4 Integral transforms, operational calculus (44-XX)
4 Global analysis, analysis on manifolds (58-XX)
4 Optics, electromagnetic theory (78-XX)
3 Several complex variables and analytic spaces (32-XX)
3 Relativity and gravitational theory (83-XX)
2 General and overarching topics; collections (00-XX)
2 History and biography (01-XX)
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2 Integral equations (45-XX)
2 Geophysics (86-XX)
1 Mathematical logic and foundations (03-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Commutative algebra (13-XX)
1 Nonassociative rings and algebras (17-XX)
1 \(K\)-theory (19-XX)
1 Group theory and generalizations (20-XX)
1 Topological groups, Lie groups (22-XX)
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1 Geometry (51-XX)
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1 Manifolds and cell complexes (57-XX)

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