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).

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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. Carnicer, J. M.; Khiar, Y.; Peña, J. M.: Optimal stability of the Lagrange formula and conditioning of the Newton formula (2019)
  4. Costabile, Francesco A.; Gualtieri, Maria Italia; Napoli, Anna: Recurrence relations and determinant forms for general polynomial sequences. Application to Genocchi polynomials (2019)
  5. Fasi, Massimiliano; Iannazzo, Bruno: Computing primary solutions of equations involving primary matrix functions (2019)
  6. Feng, Yuehua; Lu, Linzhang: On the growth factor upper bound for Aasen’s algorithm (2019)
  7. Huang, Rong: Accurate solutions of product linear systems associated with rank-structured matrices (2019)
  8. Lange, Marko; Rump, Siegfried M.: Sharp estimates for perturbation errors in summations (2019)
  9. Marco, Ana; Martínez, José-Javier: Accurate computation of the Moore-Penrose inverse of strictly totally positive matrices (2019)
  10. Peña, Juan Manuel; Sauer, Tomas: SVD update methods for large matrices and applications (2019)
  11. Al-Mohy, Awad H.: A truncated Taylor series algorithm for computing the action of trigonometric and hyperbolic matrix functions (2018)
  12. 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)
  13. Antoñana, Mikel; Makazaga, Joseba; Murua, Ander: Efficient implementation of symplectic implicit Runge-Kutta schemes with simplified Newton iterations (2018)
  14. Aston, John A. D.; Kirch, Claudia: High dimensional efficiency with applications to change point tests (2018)
  15. 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)
  16. Breiding, Paul; Kališnik, Sara; Sturmfels, Bernd; Weinstein, Madeleine: Learning algebraic varieties from samples (2018)
  17. Breiding, Paul; Vannieuwenhoven, Nick: A Riemannian trust region method for the canonical tensor rank approximation problem (2018)
  18. Bremer, James: An algorithm for the numerical evaluation of the associated Legendre functions that runs in time independent of degree and order (2018)
  19. Bujanović, Zvonimir; Karlsson, Lars; Kressner, Daniel: A Householder-based algorithm for Hessenberg-triangular reduction (2018)
  20. 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)

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