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).

References in zbMATH (referenced in 1423 articles )

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  1. Beccari, Carolina Vittoria; Casciola, Giulio: Matrix representations for multi-degree B-splines (2021)
  2. Bosner, Nela: Parallel reduction of four matrices to condensed form for a generalized matrix eigenvalue algorithm (2021)
  3. Breiding, Paul; Vannieuwenhoven, Nick: The condition number of Riemannian approximation problems (2021)
  4. Bujanovic, Zvonimir; Kressner, Daniel: Norm and trace estimation with random rank-one vectors (2021)
  5. Connolly, Michael P.; Higham, Nicholas J.; Mary, Theo: Stochastic rounding and its probabilistic backward error analysis (2021)
  6. Dell’Accio, Francesco; Di Tommaso, Filomena; Siar, Najoua: On the numerical computation of bivariate Lagrange polynomials (2021)
  7. Emiris, Ioannis Z.; Mantzaflaris, Angelos; Tsigaridas, Elias P.: Multilinear polynomial systems: root isolation and bit complexity (2021)
  8. Fasi, Massimiliano; Higham, Nicholas J.: Generating extreme-scale matrices with specified singular values or condition number (2021)
  9. Faßbender, Heike; Rozložník, Miroslav; Singer, Sanja: Nearly optimal scaling in the SR decomposition (2021)
  10. Ferjančič, Karla; Knez, Marjeta; Vitrih, Vito: On (\mathcalC^2) rational motions of degree six (2021)
  11. Giesbrecht, Mark; Haraldson, Joseph; Labahn, George: Computing nearby non-trivial Smith forms (2021)
  12. Hashemi, Behnam: Sufficient conditions for the solvability of a Sylvester-like absolute value matrix equation (2021)
  13. Higham, Desmond J.; Higham, Nicholas J.; Pranesh, Srikara: Random matrices generating large growth in LU factorization with pivoting (2021)
  14. Huang, Weizhang; Kamenski, Lennard; Lang, Jens: Conditioning of implicit Runge-Kutta integration for finite element approximation of linear diffusion equations on anisotropic meshes (2021)
  15. Khoury, Anthony M.; Divo, Eduardo; Golubev, Vladimir V.; Kassab, Alain J.: Meshless modeling of coupled transdermal pharmacokinetics with analytical validation (2021)
  16. Lange, Marko; Rump, Siegfried M.: Verified inclusions for a nearest matrix of specified rank deficiency via a generalization of Wedin’s (\sin(\theta)) theorem (2021)
  17. Marco, Ana; Martínez, José-Javier; Viaña, Raquel: Error analysis, perturbation theory and applications of the bidiagonal decomposition of rectangular totally positive h-Bernstein-Vandermonde matrices (2021)
  18. Mehrmann, Volker; Dooren, Paul Van: Structured backward errors for eigenvalues of linear port-Hamiltonian descriptor systems (2021)
  19. Miyajima, Shinya: Verified computation of real powers of matrices (2021)
  20. Petkov, Petko H.: Componentwise perturbation analysis of the Schur decomposition of a matrix (2021)

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