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. Abderramán Marrero, J.: On linear-time solvers for comrade linear systems (2020)
  2. Anguas, Luis Miguel; Bueno, Maria Isabel; Dopico, Froilán M.: Conditioning and backward errors of eigenvalues of homogeneous matrix polynomials under Möbius transformations (2020)
  3. Ayala, Alan; Claeys, Xavier; Grigori, Laura: Linear-time CUR approximation of BEM matrices (2020)
  4. Bevilacqua, Roberto; Del Corso, Gianna M.; Gemignani, Luca: Fast QR iterations for unitary plus low rank matrices (2020)
  5. Blanchard, Pierre; Higham, Nicholas J.; Mary, Theo: A class of fast and accurate summation algorithms (2020)
  6. Bremer, James: A quasilinear complexity algorithm for the numerical simulation of scattering from a two-dimensional radially symmetric potential (2020)
  7. Brezinski, Claude; Redivo-Zaglia, Michela: Some unusual results on extrapolation methods (2020)
  8. Chang, Xiao-Wen; Kang, Peng; Titley-Peloquin, David: Error bounds for computed least squares estimators (2020)
  9. Corless, Robert M.; Sevyeri, Leili Rafiee: The Runge example for interpolation and Wilkinson’s examples for rootfinding (2020)
  10. Cortinovis, Alice; Kressner, Daniel; Massei, Stefano: On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices (2020)
  11. Costabile, F. A.; Gualtieri, M. I.; Napoli, A.: Matrix calculus-based approach to orthogonal polynomial sequences (2020)
  12. de Camargo, André Pierro: On the numerical stability of Newton’s formula for Lagrange interpolation (2020)
  13. Del Corso, Gianna M.; Del Corso, Ilaria; Dvornicich, Roberto; Romani, Francesco: On computing the density of integers of the form (2^n + p) (2020)
  14. Dudko, Artem; Sutherland, Scott: On the Lebesgue measure of the Feigenbaum Julia set (2020)
  15. Elsworth, Steven; Güttel, Stefan: The block rational Arnoldi method (2020)
  16. Fika, Paraskevi; Mitrouli, Marilena; Roupa, Paraskevi; Triantafyllou, Dimitrios: The e-MoM approach for approximating matrix functionals (2020)
  17. Fukaya, Takeshi; Kannan, Ramaseshan; Nakatsukasa, Yuji; Yamamoto, Yusaku; Yanagisawa, Yuka: Shifted Cholesky QR for computing the QR factorization of ill-conditioned matrices (2020)
  18. Iakymchuk, Roman; Barreda, Maria; Wiesenberger, Matthias; Aliaga, José I.; Quintana-Ortí, Enrique S.: Reproducibility strategies for parallel preconditioned conjugate gradient (2020)
  19. Jawecki, Tobias; Auzinger, Winfried; Koch, Othmar: Computable upper error bounds for Krylov approximations to matrix exponentials and associated (\varphi)-functions (2020)
  20. Jeannerod, Claude-Pierre: The relative accuracy of ((x+y)*(x-y)) (2020)

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