# 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).

#### SOFTWARE DOWNLOAD

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

Statistics Links

Mathematical Software
my home page
(http://www.mat.univie.ac.at/~neum)

Arnold Neumaier (Arnold.Neumaier@univie.ac.at)