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 375 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. Aurentz, Jared L.; Austin, Anthony P.; Benzi, Michele; Kalantzis, Vassilis: Stable computation of generalized matrix functions via polynomial interpolation (2019)
  3. Bhatia, Rajendra; Congedo, Marco: Procrustes problems in Riemannian manifolds of positive definite matrices (2019)
  4. Bini, Dario A.; Meini, Beatrice: On the exponential of semi-infinite quasi-Toeplitz matrices (2019)
  5. Burgelman, Jeroen; Vanhoucke, Mario: Computing project makespan distributions: Markovian PERT networks revisited (2019)
  6. Danca, Marius; Fečkan, Michal; Pospíšil, Michal: Difference equations with impulses (2019)
  7. 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)
  8. Fasi, Massimiliano; Iannazzo, Bruno: Computing primary solutions of equations involving primary matrix functions (2019)
  9. Ghaderi, Pedram; Amini, Fereidoun: A new method for online identification of civil structures: virtual synchronization (2019)
  10. Jebreen, Haifa Bin: A Gaussian radial basis function-finite difference technique to simulate the HCIR equation (2019)
  11. Lebtahi, Leila; Romero, Óscar; Thome, Néstor: Further results on generalized centro-invertible matrices (2019)
  12. Lyu, Shulin; Griffin, James; Chen, Yang: The Hankel determinant associated with a singularly perturbed Laguerre unitary ensemble (2019)
  13. Miyajima, Shinya: Verified computation for the Hermitian positive definite solution of the conjugate discrete-time algebraic Riccati equation (2019)
  14. Aceto, Lidia; Novati, Paolo: Efficient implementation of rational approximations to fractional differential operators (2018)
  15. Al-Mohy, Awad H.: A truncated Taylor series algorithm for computing the action of trigonometric and hyperbolic matrix functions (2018)
  16. Alqahtani, Hessah; Reichel, Lothar: Simplified anti-Gauss quadrature rules with applications in linear algebra (2018)
  17. Alqahtani, Hessah; Reichel, Lothar: Multiple orthogonal polynomials applied to matrix function evaluation (2018)
  18. Andén, Joakim; Singer, Amit: Structural variability from noisy tomographic projections (2018)
  19. Antezana, Jorge; Chiumiento, Eduardo: Approximation by partial isometries and symmetric approximation of finite frames (2018)
  20. Arrigo, Francesca; Grindrod, Peter; Higham, Desmond J.; Noferini, Vanni: On the exponential generating function for non-backtracking walks (2018)

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