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 425 articles , 1 standard article )

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  1. Alhomaidhi, Alhanouf; Al-Thukair, Fawzi; Estrada, Ernesto: Gaussianization of the spectra of graphs and networks. Theory and applications (2019)
  2. Arslan, Bahar; Noferini, Vanni; Tisseur, FrançOise: The structured condition number of a differentiable map between matrix manifolds, with applications (2019)
  3. Aurentz, Jared L.; Austin, Anthony P.; Benzi, Michele; Kalantzis, Vassilis: Stable computation of generalized matrix functions via polynomial interpolation (2019)
  4. Auzinger, Winfried; Hofstätter, Harald; Koch, Othmar: Symmetrized local error estimators for time-reversible one-step methods in nonlinear evolution equations (2019)
  5. Bhatia, Rajendra; Congedo, Marco: Procrustes problems in Riemannian manifolds of positive definite matrices (2019)
  6. Bhatia, Rajendra; Jain, Tanvi; Lim, Yongdo: On the Bures-Wasserstein distance between positive definite matrices (2019)
  7. Bini, Dario A.; Massei, Stefano; Robol, Leonardo: Quasi-Toeplitz matrix arithmetic: a MATLAB toolbox (2019)
  8. Bini, Dario A.; Meini, Beatrice: On the exponential of semi-infinite quasi-Toeplitz matrices (2019)
  9. Brezinski, Claude; Redivo-Zaglia, Michela: Matrix Shanks transformations (2019)
  10. Burgelman, Jeroen; Vanhoucke, Mario: Computing project makespan distributions: Markovian PERT networks revisited (2019)
  11. Cardoso, João R.; Sadeghi, Amir: Computation of matrix gamma function (2019)
  12. Cătinaş, Emil: A survey on the high convergence orders and computational convergence orders of sequences (2019)
  13. Cheng, Hao-Chung; Hsieh, Min-Hsiu: Matrix Poincaré, $\Phi$-Sobolev inequalities, and quantum ensembles (2019)
  14. Cuchta, Tom; Grow, David; Wintz, Nick: A dynamic matrix exponential via a matrix cylinder transformation (2019)
  15. Danca, Marius; Fečkan, Michal; Pospíšil, Michal: Difference equations with impulses (2019)
  16. Das, Kinkar Ch.; Hosseinzadeh, Mohammad Ali; Hossein-Zadeh, Samaneh; Iranmanesh, Ali: Some bounds for total communicability of graphs (2019)
  17. Defez, Emilio; Ibáñez, Javier; Peinado, Jesús; Sastre, Jorge; Alonso-Jordá, Pedro: An efficient and accurate algorithm for computing the matrix cosine based on new Hermite approximations (2019)
  18. Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua: Maximum principle preserving exponential time differencing schemes for the nonlocal Allen-Cahn equation (2019)
  19. Fasi, Massimiliano: Optimality of the paterson-stockmeyer method for evaluating matrix polynomials and rational matrix functions (2019)
  20. Fasi, Massimiliano; Higham, Nicholas J.: An arbitrary precision scaling and squaring algorithm for the matrix exponential (2019)

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