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. Giesbrecht, Mark; Haraldson, Joseph; Labahn, George: Computing nearby non-trivial Smith forms (2021)
  3. Abderramán Marrero, J.: On linear-time solvers for comrade linear systems (2020)
  4. Al-Baali, Mehiddin; Caliciotti, Andrea; Fasano, Giovanni; Roma, Massimo: A class of approximate inverse preconditioners based on Krylov-subspace methods for large-scale nonconvex optimization (2020)
  5. Anguas, Luis Miguel; Bueno, Maria Isabel; Dopico, Froilán M.: Conditioning and backward errors of eigenvalues of homogeneous matrix polynomials under Möbius transformations (2020)
  6. Ayala, Alan; Claeys, Xavier; Grigori, Laura: Linear-time CUR approximation of BEM matrices (2020)
  7. Benzi, Michele; Fika, Paraskevi; Mitrouli, Marilena: Performance and stability of direct methods for computing generalized inverses of the graph Laplacian (2020)
  8. Bevilacqua, Roberto; Del Corso, Gianna M.; Gemignani, Luca: Fast QR iterations for unitary plus low rank matrices (2020)
  9. Blanchard, Pierre; Higham, Nicholas J.; Lopez, Florent; Mary, Theo; Pranesh, Srikara: Mixed precision block fused multiply-add: error analysis and application to GPU tensor cores (2020)
  10. Blanchard, Pierre; Higham, Nicholas J.; Mary, Theo: A class of fast and accurate summation algorithms (2020)
  11. Bremer, James: A quasilinear complexity algorithm for the numerical simulation of scattering from a two-dimensional radially symmetric potential (2020)
  12. Brezinski, Claude; Redivo-Zaglia, Michela: Some unusual results on extrapolation methods (2020)
  13. Chang, Xiao-Wen; Kang, Peng; Titley-Peloquin, David: Error bounds for computed least squares estimators (2020)
  14. Corless, Robert M.; Sevyeri, Leili Rafiee: The Runge example for interpolation and Wilkinson’s examples for rootfinding (2020)
  15. Cortinovis, Alice; Kressner, Daniel; Massei, Stefano: On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices (2020)
  16. Costabile, F. A.; Gualtieri, M. I.; Napoli, A.: Matrix calculus-based approach to orthogonal polynomial sequences (2020)
  17. de Camargo, André Pierro: Rounding error analysis of divided differences schemes: Newton’s divided differences; Neville’s algorithm; Richardson extrapolation; Romberg quadrature; etc. (2020)
  18. de Camargo, André Pierro: On the numerical stability of Newton’s formula for Lagrange interpolation (2020)
  19. Del Corso, Gianna M.; Del Corso, Ilaria; Dvornicich, Roberto; Romani, Francesco: On computing the density of integers of the form (2^n + p) (2020)
  20. Dudko, Artem; Sutherland, Scott: On the Lebesgue measure of the Feigenbaum Julia set (2020)

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