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. Beccari, Carolina Vittoria; Casciola, Giulio: Matrix representations for multi-degree B-splines (2021)
  2. Bénéteau, Catherine; Manolaki, Myrto; Seco, Daniel: Boundary behavior of optimal polynomial approximants (2021)
  3. Bialecki, Bernard; Dryja, Maksymilian; Fernandes, Ryan I.: Convergence analysis of the finite difference ADI scheme for the heat equation on a convex set (2021)
  4. Bojanczyk, Adam W.: Algorithms for indefinite linear least squares problems (2021)
  5. Bosner, Nela: Parallel reduction of four matrices to condensed form for a generalized matrix eigenvalue algorithm (2021)
  6. Bosner, Nela: Parallel Prony’s method with multivariate matrix pencil approach and its numerical aspects (2021)
  7. Breiding, Paul; Vannieuwenhoven, Nick: The condition number of Riemannian approximation problems (2021)
  8. Bujanovic, Zvonimir; Kressner, Daniel: Norm and trace estimation with random rank-one vectors (2021)
  9. Bünger, Alexandra; Simoncini, Valeria; Stoll, Martin: A low-rank matrix equation method for solving PDE-constrained optimization problems (2021)
  10. Casulli, Angelo; Robol, Leonardo: Rank-structured QR for Chebyshev rootfinding (2021)
  11. Cătinaş, Emil: How many steps still left to (x)? (2021)
  12. Connolly, Michael P.; Higham, Nicholas J.; Mary, Theo: Stochastic rounding and its probabilistic backward error analysis (2021)
  13. Dell’Accio, Francesco; Di Tommaso, Filomena; Siar, Najoua: On the numerical computation of bivariate Lagrange polynomials (2021)
  14. Emiris, Ioannis Z.; Mantzaflaris, Angelos; Tsigaridas, Elias P.: Multilinear polynomial systems: root isolation and bit complexity (2021)
  15. Fasi, Massimiliano; Higham, Nicholas J.: Matrices with tunable infinity-norm condition number and no need for pivoting in LU factorization (2021)
  16. Fasi, Massimiliano; Higham, Nicholas J.: Generating extreme-scale matrices with specified singular values or condition number (2021)
  17. Faßbender, Heike; Rozložník, Miroslav; Singer, Sanja: Nearly optimal scaling in the SR decomposition (2021)
  18. Ferjančič, Karla; Knez, Marjeta; Vitrih, Vito: On (\mathcalC^2) rational motions of degree six (2021)
  19. Gautier, Antoine; Hein, Matthias; Tudisco, Francesco: The global convergence of the nonlinear power method for mixed-subordinate matrix norms (2021)
  20. Gawlik, Evan S.: Rational minimax iterations for computing the matrix (p)th root (2021)

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