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.

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  1. Alonso, Pedro; Ibáñez, Javier; Sastre, Jorge; Peinado, Jesús; Defez, Emilio: Efficient and accurate algorithms for computing matrix trigonometric functions (2017)
  2. Benzi, Michele; Simoncini, Valeria: Approximation of functions of large matrices with Kronecker structure (2017)
  3. Fenu, Caterina; Higham, Desmond J.: Block matrix formulations for evolving networks (2017)
  4. Oste, Roy; Van der Jeugt, Joris: Tridiagonal test matrices for eigenvalue computations: two-parameter extensions of the Clement matrix (2017)
  5. Arrigo, Francesca; Benzi, Michele: Updating and downdating techniques for optimizing network communicability (2016)
  6. Delgado, Jorge; Peña, Guillermo; Peña, Juan Manuel: Accurate and fast computations with positive extended Schoenmakers-Coffey matrices. (2016)
  7. Li, Wen; Xie, Ze-Jia; Vong, Seak-Weng: Sensitivity analysis for the symplectic QR factorization (2016)
  8. Luo, Ziyan; Qi, Liqun: Completely positive tensors: properties, easily checkable subclasses, and tractable relaxations (2016)
  9. Oste, Roy; Van der Jeugt, Joris: Doubling (dual) Hahn polynomials: classification and applications (2016)
  10. Arioli, Mario; Duff, Iain S.: Preconditioning linear least-squares problems by identifying a basis matrix (2015)
  11. Benzi, Michele; Kuhlemann, Verena: Chebyshev acceleration of the GeneRank algorithm (2013)
  12. Defez, Emilio; Sastre, Jorge; Ibáñez, Javier; Ruiz, Pedro: Computing matrix functions arising in engineering models with orthogonal matrix polynomials (2013)
  13. Wu, Gang; Xu, Wei; Zhang, Ying; Wei, Yimin: A preconditioned conjugate gradient algorithm for GeneRank with application to microarray data mining (2013)
  14. Wu, Gang; Zhang, Ying; Wei, Yimin: Accelerating the Arnoldi-type algorithm for the PageRank problem and the ProteinRank problem (2013)
  15. Liu, Xin-Guo; Zhao, Na: Linearization estimates of the backward errors for least squares problems. (2012)
  16. Redivo-Zaglia, Michela; Rodriguez, Giuseppe: smt: A Matlab toolbox for structured matrices (2012)
  17. Carvalho, João B.; Datta, Biswa N.: A new algorithm for generalized Sylvester-observer equation and its application to state and velocity estimations in vibrating systems. (2011)
  18. Gemignani, L.: On some classes of structured matrices with algebraic trigonometric eigenvalues (2011)
  19. Lu, Chengbo; Gu, Chuanqing: The computation of the square roots of circulant matrices (2011)
  20. Sastre, J.; Ibáñez, J.; Defez, E.; Ruiz, P.: Efficient orthogonal matrix polynomial based method for computing matrix exponential (2011)

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