Re: Nonsymmetric eigenvalue problem

[Brian Gough <bjg at network-theory dot co dot uk>]

Lowell Johnson writes:
 > I notice that GSL doesn't (yet) support the computation of the
 > eigenvalues of nonsymmetric matrices.  I've started converting my
 > Fortran-based Mathieu function code over to C and ran into the
 > symmetric eigenvalue limitation in GSL.  For my original Fortran
 > routines, I used the EISPACK routine RG(), which computes the
 > eigenvalues and eigenvectors of a real, general matrix.  I was
 > hoping to be able to use the GSL eigenvalue routines.  I have to
 > determine the eigenvalues for four matrices.  The one listed above
 > is the only nonsymmetric matrix.  The GSL routines work great for
 > the other three matrices.
 >  Any comments or suggestions?

The algorithm for non-symmetric eigenvalues is very complicated, which
is why it wasn't implemented.  Maybe there is a simpler algorithm for
handling tridiagonal nonsymmetric matrices though.

What method does Fayez Alhargan use in the TOMS papers?