The Matrix Computation Toolbox

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).

The picture on the left, produced by toolbox function pscont, shows a view of pseudospectra of the matrix gallery('triw',11).

The toolbox is distributed under the terms of the GNU General Public License (version 3 of the License, or any later version) as published by the Free Software Foundation.

The toolbox has been tested under MATLAB 6.1 (R12.1) and MATLAB 6.5 (R13). For how to overcome a minor incompatibility with MATLAB 6.1 and earlier see the updates link below.

The M-files in the toolbox are self-documenting and so more detailed documentation than is provided here can be obtained on­line by typing help M-file_name.

The current release is version 1.2 of the toolbox, dated September 5, 2002.

The Toolbox

• The toolbox is provided as a zip file, which can be uncompressed with any zip file utility.
• Documentation, including installation instructions, release history, and quick reference tables, is provided in the document mctoolbox.pdf located within the zip file.
• Please cite the toolbox as "N. J. Higham. The Matrix Computation Toolbox. http://www.ma.man.ac.uk/~higham/mctoolbox". A BibTeX bib entry for this book is available.
• Updates, bugs, release history.
• A predecessor of this toolbox is the Test Matrix Toolbox (version 3.0, 1995), which is available as a zip file with documentation, and is distributed under the terms of the GNU General Public License (version 3 of the License, or any later version) as published by the Free Software Foundation.

Related Links

• MATLAB Guide, by Nicholas J. Higham and Desmond J. Higham (SIAM, 2000) documents all the matrices in MATLAB, including those that are part of the gallery function.
• Accuracy and Stability of Numerical Algorithms (Second edition, SIAM, August 2002, xxx+680 pp.).
• A more efficient and versatile MATLAB tool for plotting pseudospectra is Tom Wright's eigtool.