mftoolbox

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.


References in zbMATH (referenced in 612 articles , 1 standard article )

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  1. Al-Mohy, Awad H.; Higham, Nicholas J.; Liu, Xiaobo: Arbitrary precision algorithms for computing the matrix cosine and its Fréchet derivative (2022)
  2. Antoine, X.; Lorin, E.: Generalized fractional algebraic linear system solvers (2022)
  3. Benner, Peter; Penke, Carolin: Efficient and accurate algorithms for solving the Bethe-Salpeter eigenvalue problem for crystalline systems (2022)
  4. Benzi, Michele; Simunec, Igor: Rational Krylov methods for fractional diffusion problems on graphs (2022)
  5. Boito, Paola; Eidelman, Yuli; Gemignani, Luca: Computing the reciprocal of a (\phi)-function by rational approximation (2022)
  6. Bolsinov, Alexey V.; Konyaev, Andrey Yu.; Matveev, Vladimir S.: Nijenhuis geometry (2022)
  7. Cardoso, João R.; Miraldo, Pedro: Solving the discrete Euler-Arnold equations for the generalized rigid body motion (2022)
  8. Cortinovis, Alice; Kressner, Daniel; Massei, Stefano: Divide-and-conquer methods for functions of matrices with banded or hierarchical low-rank structure (2022)
  9. Defez, E.; Ibáñez, J.; Peinado, J.; Alonso-Jordá, P.; Alonso, José M.: New Hermite series expansion for computing the matrix hyperbolic cosine (2022)
  10. De la Cruz Cabrera, Omar; Jin, Jiafeng; Noschese, Silvia; Reichel, Lothar: Communication in complex networks (2022)
  11. Dendievel, Sarah; Latouche, Guy; Liu, Yuanyuan; Tang, Yingchun: Singularly perturbed Markov modulated fluid queues (2022)
  12. Dinčić, Nebojša Č.; Djordjević, Bogdan D.: On the intrinsic structure of the solution set to the Yang-Baxter-like matrix equation (2022)
  13. Djete, Mao Fabrice: Extended mean field control problem: a propagation of chaos result (2022)
  14. Estrada, Ernesto: The many facets of the Estrada indices of graphs and networks (2022)
  15. Farooq, Asma; Maset, Stefano: How perturbations in the matrix of linear systems of ordinary differential equations propagate along solutions (2022)
  16. Hannani, Amirali: Hydrodynamic limit for a disordered quantum harmonic chain (2022)
  17. Hao, Pengwei; Zhang, Chao; Hao, Huahan: Zero-sum triangles for involutory, idempotent, nilpotent and unipotent matrices (2022)
  18. Jiang, Chaolong; Cui, Jin; Qian, Xu; Song, Songhe: High-order linearly implicit structure-preserving exponential integrators for the nonlinear Schrödinger equation (2022)
  19. Kumar, Ashim; Cardoso, João R.; Singh, Gurjinder: Explicit solutions of the singular Yang-Baxter-like matrix equation and their numerical computation (2022)
  20. Li, Dongping; Yang, Siyu; Lan, Jiamei: Efficient and accurate computation for the (\varphi)-functions arising from exponential integrators (2022)

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