The Matrix Computation Toolbox is a collection of MATLAB M-files containing functions for constructing test matrices, computing matrix factorizations, visualizing matrices, and carrying out direct search optimization. Various other miscellaneous functions are also included. This toolbox supersedes the author’s earlier Test Matrix Toolbox (final release 1995). The toolbox was developed in conjunction with the book Accuracy and Stability of Numerical Algorithms (SIAM, Second edition, August 2002, xxx+680 pp.). That book is the primary documentation for the toolbox: it describes much of the underlying mathematics and many of the algorithms and matrices (it also describes many of the matrices provided by MATLAB’s gallery function).

References in zbMATH (referenced in 1317 articles )

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  1. Ayala, Alan; Claeys, Xavier; Grigori, Laura: Linear-time CUR approximation of BEM matrices (2020)
  2. Bevilacqua, Roberto; Del Corso, Gianna M.; Gemignani, Luca: Fast QR iterations for unitary plus low rank matrices (2020)
  3. Jeannerod, Claude-Pierre: The relative accuracy of (\mathtt(x+y)*(x-y)) (2020)
  4. Jia, Ji-Teng: A breakdown-free algorithm for computing the determinants of periodic tridiagonal matrices (2020)
  5. Kozioł, Kamil; Stanisławski, Rafał: Selected implementation issues in computation of the Grünwald-Letnikov fractional-order difference by means of embedded system (2020)
  6. Meng, Qingle; Diao, Huaian; Yu, Qinghua: Structured condition number for multiple right-hand side linear systems with parameterized quasiseparable coefficient matrix (2020)
  7. Ogita, Takeshi; Aishima, Kensuke: Iterative refinement for singular value decomposition based on matrix multiplication (2020)
  8. Alonso, P.; Peña, J. M.; Serrano, M. L.: Comparing pivoting strategies for almost strictly sign regular matrices (2019)
  9. Arslan, Bahar; Noferini, Vanni; Tisseur, Françoise: The structured condition number of a differentiable map between matrix manifolds, with applications (2019)
  10. Aurentz, Jared L.; Austin, Anthony P.; Benzi, Michele; Kalantzis, Vassilis: Stable computation of generalized matrix functions via polynomial interpolation (2019)
  11. Aurentz, Jared; Mach, Thomas; Robol, Leonardo; Vandebril, Raf; Watkins, David S.: Fast and backward stable computation of eigenvalues and eigenvectors of matrix polynomials (2019)
  12. Barlow, Jesse L.: Block modified Gram-Schmidt algorithms and their analysis (2019)
  13. Beltrán, Carlos; Breiding, Paul; Vannieuwenhoven, Nick: Pencil-based algorithms for tensor rank decomposition are not stable (2019)
  14. Berahas, Albert S.; Byrd, Richard H.; Nocedal, Jorge: Derivative-free optimization of noisy functions via quasi-Newton methods (2019)
  15. Birgin, E. G.; Martínez, J. M.: A Newton-like method with mixed factorizations and cubic regularization for unconstrained minimization (2019)
  16. Bremer, James: An algorithm for the rapid numerical evaluation of Bessel functions of real orders and arguments (2019)
  17. Brezinski, Claude; Redivo-Zaglia, Michela: Matrix Shanks transformations (2019)
  18. Caliari, M.; Zivcovich, F.: On-the-fly backward error estimate for matrix exponential approximation by Taylor algorithm (2019)
  19. Cambier, Léopold; Darve, Eric: Fast low-rank kernel matrix factorization using skeletonized interpolation (2019)
  20. Carbone, Maurizio; Iovieno, Michele: Application of the nonuniform fast Fourier transform to the direct numerical simulation of two-way coupled particle laden flows (2019)

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