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 555 articles , 1 standard article )

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  1. Benner, Peter; Penke, Carolin: Efficient and accurate algorithms for solving the Bethe-Salpeter eigenvalue problem for crystalline systems (2022)
  2. Abdalla, Mohamed; Boulaaras, Salah Mahmoud: Analytical properties of the generalized heat matrix polynomials associated with fractional calculus (2021)
  3. Abdalla, Mohamed; Hidan, Muajebah: Analytical properties of the two-variables Jacobi matrix polynomials with applications (2021)
  4. Al-Mohy, Awad H.; Arslan, Bahar: The complex step approximation to the higher order Fréchet derivatives of a matrix function (2021)
  5. Al Mugahwi, Mohammed; De la Cruz Cabrera, Omar; Noschese, Silvia; Reichel, Lothar: Functions and eigenvectors of partially known matrices with applications to network analysis (2021)
  6. Beckermann, Bernhard; Cortinovis, Alice; Kressner, Daniel; Schweitzer, Marcel: Low-rank updates of matrix functions. II: Rational Krylov methods (2021)
  7. Benner, Peter; Werner, Steffen W. R.: Frequency- and time-limited balanced truncation for large-scale second-order systems (2021)
  8. Benzi, Michele: Some uses of the field of values in numerical analysis (2021)
  9. Bergermann, Kai; Stoll, Martin; Volkmer, Toni: Semi-supervised learning for aggregated multilayer graphs using diffuse interface methods and fast matrix-vector products (2021)
  10. Botchev, M. A.: An accurate restarting for shift-and-invert Krylov subspaces computing matrix exponential actions of nonsymmetric matrices (2021)
  11. Chen, Hao; Sun, Hai-Wei: A dimensional splitting exponential time differencing scheme for multidimensional fractional Allen-Cahn equations (2021)
  12. Chen, Pengwen; Cheng, Chung-Kuan; Wang, Xinyuan: Arnoldi algorithms with structured orthogonalization (2021)
  13. Chow, Kevin; Ruuth, Steven J.: Linearly stabilized schemes for the time integration of stiff nonlinear PDEs (2021)
  14. De la Cruz Cabrera, Omar; Matar, Mona; Reichel, Lothar: Centrality measures for node-weighted networks via line graphs and the matrix exponential (2021)
  15. Ding, Zhiyan; Li, Qin: Ensemble Kalman sampler: mean-field limit and convergence analysis (2021)
  16. Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua: Maximum bound principles for a class of semilinear parabolic equations and exponential time-differencing schemes (2021)
  17. Frommer, Andreas; Schimmel, Claudia; Schweitzer, Marcel: Analysis of probing techniques for sparse approximation and trace estimation of decaying matrix functions (2021)
  18. Fu, Yayun; Xu, Zhuangzhi; Cai, Wenjun; Wang, Yushun: An efficient energy-preserving method for the two-dimensional fractional Schrödinger equation (2021)
  19. Gawlik, Evan S.: Rational minimax iterations for computing the matrix (p)th root (2021)
  20. Gawlik, Evan S.; Nakatsukasa, Yuji: Approximating the (p)th root by composite rational functions (2021)

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