The Test Matrix Toolbox for MATLAB. We describe version 3.0 of the Test Matrix Toolbox for Matlab 4.2. The toolbox contains a collection of test matrices, routines for visualizing matrices, routines for direct search optimization, and miscellaneous routines that provide useful additions to Matlab’s existing set of functions. There are 58 parametrized test matrices, which are mostly square, dense, nonrandom, and of arbitrary dimension. The test matrices include ones with known inverses or known eigenvalues; ill-conditioned or rank deficient matrices; and symmetric, positive definite, orthogonal, defective, involutary, and totally positive matrices. The visualization routines display surface plots of a matrix and its (pseudo-) inverse, the field of values, Gershgorin disks, and two- and three-dimensional views of pseudospectra. The direct search optimization routines implement the alternating directions method, the multidirectional search method and the Nelder--Mead simplex method.

References in zbMATH (referenced in 84 articles )

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  1. Boito, Paola; Eidelman, Yuli; Gemignani, Luca: Computing the reciprocal of a (\phi)-function by rational approximation (2022)
  2. Fatemi, Masoud: On initial point selection of the steepest descent algorithm for general quadratic functions (2022)
  3. Guo, Yongyan; Wu, Gang: A new lower bound on the size of the smallest vertex separator of a graph (2022)
  4. Liao, Zeyu; Hayami, Ken; Morikuni, Keiichi; Yin, Jun-Feng: A stabilized GMRES method for singular and severely ill-conditioned systems of linear equations (2022)
  5. Fasi, Massimiliano; Higham, Nicholas J.: Generating extreme-scale matrices with specified singular values or condition number (2021)
  6. Higham, Desmond J.; Mantzaris, Alexander V.: A network model for polarization of political opinion (2020)
  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. Sastre, Jorge; Ibáñez, Javier; Alonso-Jordá, Pedro; Peinado, Jesús; Defez, Emilio: Fast Taylor polynomial evaluation for the computation of the matrix cosine (2019)
  9. Arrigo, Francesca; Grindrod, Peter; Higham, Desmond J.; Noferini, Vanni: On the exponential generating function for non-backtracking walks (2018)
  10. Defez, Emilio; Ibáñez, Javier; Sastre, Jorge; Peinado, Jesús; Alonso, Pedro: A new efficient and accurate spline algorithm for the matrix exponential computation (2018)
  11. Grindrod, Peter; Higham, Desmond J.; Noferini, Vanni: The deformed graph Laplacian and its applications to network centrality analysis (2018)
  12. Alonso, Pedro; Ibáñez, Javier; Sastre, Jorge; Peinado, Jesús; Defez, Emilio: Efficient and accurate algorithms for computing matrix trigonometric functions (2017)
  13. Benzi, Michele; Simoncini, Valeria: Approximation of functions of large matrices with Kronecker structure (2017)
  14. Fenu, Caterina; Higham, Desmond J.: Block matrix formulations for evolving networks (2017)
  15. Oste, Roy; Van der Jeugt, Joris: Tridiagonal test matrices for eigenvalue computations: two-parameter extensions of the Clement matrix (2017)
  16. Sastre, Jorge; Ibáñez, Javier; Alonso, Pedro; Peinado, Jesús; Defez, Emilio: Two algorithms for computing the matrix cosine function (2017)
  17. Arrigo, Francesca; Benzi, Michele: Updating and downdating techniques for optimizing network communicability (2016)
  18. Delgado, Jorge; Peña, Guillermo; Peña, Juan Manuel: Accurate and fast computations with positive extended Schoenmakers-Coffey matrices. (2016)
  19. Li, Wen; Xie, Ze-Jia; Vong, Seak-Weng: Sensitivity analysis for the symplectic QR factorization (2016)
  20. Luo, Ziyan; Qi, Liqun: Completely positive tensors: properties, easily checkable subclasses, and tractable relaxations (2016)

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