mctoolbox

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 1199 articles )

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  1. Aurentz, Jared; Mach, Thomas; Robol, Leonardo; Vandebril, Raf; Watkins, David S.: Fast and backward stable computation of eigenvalues and eigenvectors of matrix polynomials (2019)
  2. Caliari, M.; Zivcovich, F.: On-the-fly backward error estimate for matrix exponential approximation by Taylor algorithm (2019)
  3. Lange, Marko; Rump, Siegfried M.: Sharp estimates for perturbation errors in summations (2019)
  4. Al-Mohy, Awad H.: A truncated Taylor series algorithm for computing the action of trigonometric and hyperbolic matrix functions (2018)
  5. Antoñana, Mikel; Makazaga, Joseba; Murua, Ander: New integration methods for perturbed ODEs based on symplectic implicit Runge-Kutta schemes with application to solar system simulations (2018)
  6. Antoñana, Mikel; Makazaga, Joseba; Murua, Ander: Efficient implementation of symplectic implicit Runge-Kutta schemes with simplified Newton iterations (2018)
  7. Aston, John A. D.; Kirch, Claudia: High dimensional efficiency with applications to change point tests (2018)
  8. Aurentz, Jared L.; Mach, Thomas; Robol, Leonardo; Vandebril, Raf; Watkins, David S.: Fast and backward stable computation of roots of polynomials. II: Backward error analysis; companion matrix and companion pencil (2018)
  9. Breiding, Paul; Kališnik, Sara; Sturmfels, Bernd; Weinstein, Madeleine: Learning algebraic varieties from samples (2018)
  10. Breiding, Paul; Vannieuwenhoven, Nick: A Riemannian trust region method for the canonical tensor rank approximation problem (2018)
  11. Bremer, James: An algorithm for the numerical evaluation of the associated Legendre functions that runs in time independent of degree and order (2018)
  12. Bujanović, Zvonimir; Karlsson, Lars; Kressner, Daniel: A Householder-based algorithm for Hessenberg-triangular reduction (2018)
  13. Carson, Erin C.; Rozložník, Miroslav; Strakoš, Zdeněk; Tichý, Petr; Tuma, Miroslav: The numerical stability analysis of pipelined conjugate gradient methods: historical context and methodology (2018)
  14. Carson, Erin; Higham, Nicholas J.: Accelerating the solution of linear systems by iterative refinement in three precisions (2018)
  15. Coelho, Diego F. G.; Dimitrov, Vassil S.; Rakai, L.: Efficient computation of tridiagonal matrices largest eigenvalue (2018)
  16. Cools, Siegfried; Yetkin, Emrullah Fatih; Agullo, Emmanuel; Giraud, Luc; Vanroose, Wim: Analyzing the effect of local rounding error propagation on the maximal attainable accuracy of the pipelined conjugate gradient method (2018)
  17. Coutinho, S. C.: Bounding the degree of solutions of differential equations (2018)
  18. D’Amore, Luisa; Mele, Valeria; Campagna, Rosanna: Quality assurance of Gaver’s formula for multi-precision Laplace transform inversion in real case (2018)
  19. D’Amore, Luisa; Romano, Diego: An objective criterion for stopping light-surface interaction. Numerical validation and quality assessment (2018)
  20. Defez, Emilio; Ibáñez, Javier; Sastre, Jorge; Peinado, Jesús; Alonso, Pedro: A new efficient and accurate spline algorithm for the matrix exponential computation (2018)

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