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 511 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. Chen, Pengwen; Cheng, Chung-Kuan; Wang, Xinyuan: Arnoldi algorithms with structured orthogonalization (2021)
  3. 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)
  4. He, Xiaodong; Geng, Zhiyong: Consensus-based formation control for nonholonomic vehicles with parallel desired formations (2021)
  5. Jagels, Carl; Jbilou, Khalide; Reichel, Lothar: The extended global Lanczos method, Gauss-Radau quadrature, and matrix function approximation (2021)
  6. Li, Dongping; Zhang, Xiuying; Liu, Renyun: Exponential integrators for large-scale stiff Riccati differential equations (2021)
  7. Liu, Hai-Feng: Frame completion with prescribed norms via alternating projection method (2021)
  8. Lorin, Emmanuel; Tian, Simon: A numerical study of fractional linear algebraic systems (2021)
  9. Luan, Vu Thai; Michels, Dominik L.: Efficient exponential time integration for simulating nonlinear coupled oscillators (2021)
  10. Miyajima, Shinya: Verified computation of real powers of matrices (2021)
  11. Pan, Mingyang; Wang, Qinghe; He, Dongdong; Pan, Kejia: Positive-definiteness preserving and energy stable time-marching scheme for a diffusive Oldroyd-B electrohydrodynamic model (2021)
  12. Seydaoğlu, Muaz; Bader, Philipp; Blanes, Sergio; Casas, Fernando: Computing the matrix sine and cosine simultaneously with a reduced number of products (2021)
  13. Skripka, Anna: MSE bounds for estimators of matrix functions (2021)
  14. Soleymani, Fazlollah; Zhu, Shengfeng: RBF-FD solution for a financial partial-integro differential equation utilizing the generalized multiquadric function (2021)
  15. Vabishchevich, P. N.: An approximate representation of a solution to fractional elliptical BVP via solution of parabolic IVP (2021)
  16. Wu, Gang; Li, Fei: A randomized exponential canonical correlation analysis method for data analysis and dimensionality reduction (2021)
  17. Yang, Junjian; Lu, Linzhang: Weighted geometric mean of two accretive matrices (2021)
  18. Abdalla, Mohamed: Special matrix functions: characteristics, achievements and future directions (2020)
  19. Abderramán Marrero, J.; Aiat Hadj, D. A.: Improving formulas for the eigenvalues of finite block-Toeplitz tridiagonal matrices (2020)
  20. 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)

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