OEIG - Solving overdetermined eigenvalue problems

DESCRIPTION

OEIG is a MATLAB based software to solve the overdetermined generalized eigenvalue problem
(A - &lambda B)v &asymp 0,
where A and B are m x n matrices with m > n, i.e., more rows than columns. Usually the matrix A - &lambda B has full rank. Therefore we aim to compute &lambda for which A - &lambda B is as close as possible to rank deficient; i.e., we search for &lambda that locally minimize the smallest singular value of A - &lambda B.

Details about the method and experimental results are available in the manuscript

If you prepare publications based on programs using this software, please cite this paper (or its published version, once published).

The software is available for download as a tarball or as a zipfile. The software is compatible with MATLAB version 7 or higher. To run it requires the MATLAB optimization toolbox.

The software contains MATLAB source code of the proposed algorithm as well as drivers for demonstration, functions for simulation, and utility routines for visualization. To facilitate comparison, it also contains reimplementations of algorithms for the same purpose designed by other researchers.

USAGE

Unpack the tarball, add the location of OEIG in the MATLAB path, and it is ready to use.

The calling sequence of the main function "oeig" is written like MATLAB's "eig" function. For example if you call "oeig" with one output argument, it will return only the overdetermined eigenvalues in a vector. If you call "oeig" with two output arguments, then "oeig" will return the eigenvectros in as a column of a matrix, and the eigenvalues as entries of a diagonal matrix. Within MATLAB use ">> help oeig" for further details on usage.

For a demonstration, simply run oeig without any argument (">> oeig").

AUTHOR / BUG REPORT

This software is written by Saptarshi Das and Arnold Neumaier, without any guarantee of perfomance (though it is likely to perform very well). For queries or bug reports, contact arnold.neumaier@univie.ac.at.

Global (and Local) Optimization