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 470 articles , 1 standard article )

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  1. Abdalla, Mohamed: Special matrix functions: characteristics, achievements and future directions (2020)
  2. Abderramán Marrero, J.; Aiat Hadj, D. A.: Improving formulas for the eigenvalues of finite block-Toeplitz tridiagonal matrices (2020)
  3. Abul-Ez, M.; Abd-Elmageed, H.; Hidan, M.; Abdalla, M.: On the growth order and growth type of entire functions of several complex matrices (2020)
  4. Acebrón, Juan A.: A probabilistic linear solver based on a multilevel Monte Carlo method (2020)
  5. Ackerer, Damien; Filipović, Damir: Linear credit risk models (2020)
  6. Baake, Michael; Sumner, Jeremy: Notes on Markov embedding (2020)
  7. Bao, Sijia; Constales, Denis; De Bie, Hendrik; Mertens, Teppo: Solutions for the Lévy-Leblond or parabolic Dirac equation and its generalizations (2020)
  8. Barbarino, Giovanni; Garoni, Carlo; Serra-Capizzano, Stefano: Block generalized locally Toeplitz sequences: theory and applications in the multidimensional case (2020)
  9. Bertaccini, D.; Durastante, F.: Computing functions of very large matrices with small TT/QTT ranks by quadrature formulas (2020)
  10. Bishop, Adrian N.; Del Moral, Pierre; Niclas, Angèle: A perturbation analysis of stochastic matrix Riccati diffusions (2020)
  11. Casanellas, Marta; Fernández-Sánchez, Jesús; Roca-Lacostena, Jordi: Embeddability and rate identifiability of Kimura 2-parameter matrices (2020)
  12. Čiegis, Raimondas; Vabishchevich, Petr N.: High order numerical schemes for solving fractional powers of elliptic operators (2020)
  13. Faßbender, Heike; Halwaß, Martin: On the singular value decomposition of (skew-)involutory and (skew-)coninvolutory matrices (2020)
  14. Fika, Paraskevi; Mitrouli, Marilena; Roupa, Paraskevi; Triantafyllou, Dimitrios: The e-MoM approach for approximating matrix functionals (2020)
  15. Frommer, Andreas; Lund, Kathryn; Szyld, Daniel B.: Block Krylov subspace methods for functions of matrices. II: Modified block FOM (2020)
  16. Guo, Chun-Hua; Lu, Di: A study of Schröder’s method for the matrix (p)th root using power series expansions (2020)
  17. Hached, M.; Jbilou, K.: Numerical methods for differential linear matrix equations via Krylov subspace methods (2020)
  18. Hafner, Christian M.; Linton, Oliver B.; Tang, Haihan: Estimation of a multiplicative correlation structure in the large dimensional case (2020)
  19. Jawecki, Tobias; Auzinger, Winfried; Koch, Othmar: Computable upper error bounds for Krylov approximations to matrix exponentials and associated (\varphi)-functions (2020)
  20. Kaandorp, Mikael L. A.; Dwight, Richard P.: Data-driven modelling of the Reynolds stress tensor using random forests with invariance (2020)

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