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 L.; Austin, Anthony P.; Benzi, Michele; Kalantzis, Vassilis: Stable computation of generalized matrix functions via polynomial interpolation (2019)
  2. Aurentz, Jared; Mach, Thomas; Robol, Leonardo; Vandebril, Raf; Watkins, David S.: Fast and backward stable computation of eigenvalues and eigenvectors of matrix polynomials (2019)
  3. Caliari, M.; Zivcovich, F.: On-the-fly backward error estimate for matrix exponential approximation by Taylor algorithm (2019)
  4. Carnicer, J. M.; Khiar, Y.; Peña, J. M.: Optimal stability of the Lagrange formula and conditioning of the Newton formula (2019)
  5. Costabile, Francesco A.; Gualtieri, Maria Italia; Napoli, Anna: Recurrence relations and determinant forms for general polynomial sequences. Application to Genocchi polynomials (2019)
  6. Drineas, Petros; Ipsen, Ilse C. F.: Low-rank matrix approximations do not need a singular value gap (2019)
  7. Fasi, Massimiliano; Iannazzo, Bruno: Computing primary solutions of equations involving primary matrix functions (2019)
  8. Feng, Yuehua; Lu, Linzhang: On the growth factor upper bound for Aasen’s algorithm (2019)
  9. Higham, Nicholas J.; Pranesh, Srikara: Simulating low precision floating-point arithmetic (2019)
  10. Huang, Rong: Accurate solutions of product linear systems associated with rank-structured matrices (2019)
  11. Kressner, Daniel; Massei, Stefano; Robol, Leonardo: Low-rank updates and a divide-and-conquer method for linear matrix equations (2019)
  12. Kuřátko, Jan: Factorization of saddle-point matrices in dynamical systems optimization -- reusing pivots (2019)
  13. Lange, Marko; Rump, Siegfried M.: Sharp estimates for perturbation errors in summations (2019)
  14. Magron, Victor; Safey El Din, Mohab; Schweighofer, Markus: Algorithms for weighted sum of squares decomposition of non-negative univariate polynomials (2019)
  15. Marco, Ana; Martínez, José-Javier: Accurate computation of the Moore-Penrose inverse of strictly totally positive matrices (2019)
  16. Peña, Juan Manuel; Sauer, Tomas: SVD update methods for large matrices and applications (2019)
  17. Rossini, Jacopo; Canale, Antonio: Quantifying prediction uncertainty for functional-and-scalar to functional autoregressive models under shape constraints (2019)
  18. Wang, Min; Su, Yangfeng: A further analysis of backward error in polynomial deflation (2019)
  19. Afshin, Hamid Reza; Shojaeifard, Ali Reza: The sign-real spectral radius for real tensors (2018)
  20. Al-Mohy, Awad H.: A truncated Taylor series algorithm for computing the action of trigonometric and hyperbolic matrix functions (2018)

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