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. Ahmad, Mian Ilyas; Szyld, Daniel B.; van Gijzen, Martin B.: Preconditioned multishift BiCG for $\mathcalH_2$-optimal model reduction (2017)
  2. Brezinski, Claude; Redivo-Zaglia, Michela: The simplified topological $\varepsilon$-algorithms: software and applications (2017)
  3. de Camargo, André Pierro; Mascarenhas, Walter F.: The stability of extended Floater-Hormann interpolants (2017)
  4. Diao, Huai-An; Wei, Yimin; Xie, Pengpeng: Small sample statistical condition estimation for the total least squares problem (2017)
  5. Jeannerod, Claude-Pierre; Kornerup, Peter; Louvet, Nicolas; Muller, Jean-Michel: Error bounds on complex floating-point multiplication with an FMA (2017)
  6. Kojima, Hiroki; Matsuo, Takayasu; Furihata, Daisuke: Some discrete inequalities for central-difference type operators (2017)
  7. Mascarenhas, Walter F.; de Camargo, André Pierro: The effects of rounding errors in the nodes on barycentric interpolation (2017)
  8. Ma, Wei: On normwise structured backward errors for the generalized saddle point systems (2017)
  9. Zemke, Jens-Peter M.: Variants of IDR with partial orthonormalization (2017)
  10. Adam, Stavros P.; Magoulas, George D.; Karras, Dimitrios A.; Vrahatis, Michael N.: Bounding the search space for global optimization of neural networks learning error: an interval analysis approach (2016)
  11. Ainsworth, Mark; Sánchez, Manuel A.: Computing the Bézier control points of the Lagrangian interpolant in arbitrary dimension (2016)
  12. Aprahamian, Mary; Higham, Nicholas J.: Matrix inverse trigonometric and inverse hyperbolic functions: theory and algorithms (2016)
  13. Area, Iván; Dimitrov, Dimitar K.; Godoy, Eduardo; Paschoa, Vanessa G.: Approximate calculation of sums. II: Gaussian type quadrature (2016)
  14. Bahsoun, Wael; Galatolo, Stefano; Nisoli, Isaia; Niu, Xiaolong: Rigorous approximation of diffusion coefficients for expanding maps (2016)
  15. Ballani, Jonas; Kressner, Daniel: Reduced basis methods: from low-rank matrices to low-rank tensors (2016)
  16. Ballard, Grey; Benson, Austin R.; Druinsky, Alex; Lipshitz, Benjamin; Schwartz, Oded: Improving the numerical stability of fast matrix multiplication (2016)
  17. Biglari, Fahimeh; Mahmoodpur, Farideh: Scaling damped limited-memory updates for unconstrained optimization (2016)
  18. Caliari, Marco; Kandolf, Peter; Ostermann, Alexander; Rainer, Stefan: The Leja method revisited: backward error analysis for the matrix exponential (2016)
  19. Cardoso, João R.; Ralha, Rui: Matrix arithmetic-geometric mean and the computation of the logarithm (2016)
  20. Carrasco, Juan A.: Numerically stable methods for the computation of exit rates in Markov chains (2016)

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