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 535 articles , 1 standard article )

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  1. 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)
  2. Beckermann, Bernhard; Cortinovis, Alice; Kressner, Daniel; Schweitzer, Marcel: Low-rank updates of matrix functions II: rational Krylov methods (2021)
  3. Benner, Peter; Werner, Steffen W. R.: Frequency- and time-limited balanced truncation for large-scale second-order systems (2021)
  4. Benzi, Michele: Some uses of the field of values in numerical analysis (2021)
  5. Chen, Hao; Sun, Hai-Wei: A dimensional splitting exponential time differencing scheme for multidimensional fractional Allen-Cahn equations (2021)
  6. Chen, Pengwen; Cheng, Chung-Kuan; Wang, Xinyuan: Arnoldi algorithms with structured orthogonalization (2021)
  7. Chow, Kevin; Ruuth, Steven J.: Linearly stabilized schemes for the time integration of stiff nonlinear PDEs (2021)
  8. Ding, Zhiyan; Li, Qin: Ensemble Kalman sampler: mean-field limit and convergence analysis (2021)
  9. Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua: Maximum bound principles for a class of semilinear parabolic equations and exponential time-differencing schemes (2021)
  10. Fu, Yayun; Xu, Zhuangzhi; Cai, Wenjun; Wang, Yushun: An efficient energy-preserving method for the two-dimensional fractional Schrödinger equation (2021)
  11. Gawlik, Evan S.; Nakatsukasa, Yuji: Approximating the (p)th root by composite rational functions (2021)
  12. Groenewald, G. J.; Janse van Rensburg, D. B.; Ran, A. C. M.; Theron, F.; van Straaten, M.: (m) th roots of (H)-selfadjoint matrices (2021)
  13. He, Xiaodong; Geng, Zhiyong: Consensus-based formation control for nonholonomic vehicles with parallel desired formations (2021)
  14. Hidan, Muajebah; Akel, Mohamed; Boulaaras, Salah Mahmoud; Abdalla, Mohamed: On behavior Laplace integral operators with generalized Bessel matrix polynomials and related functions (2021)
  15. Jagels, Carl; Jbilou, Khalide; Reichel, Lothar: The extended global Lanczos method, Gauss-Radau quadrature, and matrix function approximation (2021)
  16. Jia, Zhongxiao; Wang, Fa: The convergence of the generalized Lanczos trust-region method for the trust-region subproblem (2021)
  17. Kuznetsov, Sergey V.: Abnormal dispersion of fundamental Lamb modes in FG plates. II: Symmetric versus asymmetric variation (2021)
  18. Li, Dongping; Zhang, Xiuying; Liu, Renyun: Exponential integrators for large-scale stiff Riccati differential equations (2021)
  19. Liu, Hai-Feng: Frame completion with prescribed norms via alternating projection method (2021)
  20. Lorin, Emmanuel; Tian, Simon: A numerical study of fractional linear algebraic systems (2021)

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