Re: [eigen] Lanczos Algorithm

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On 05/30/2014 08:06 AM, Imène Tendjaoui wrote:
> The Lanczos algorithm provides a tridiagonal matrix so we were wondering
> wheter it would be a good idea to use the characteristic polynomials to
> find the eigenvalues - given that the polynomials have particular
> properties - or use a more general algorithm.
> We do not know all the algorithms, so feel free to make any suggestions..

I am not an expert on this subject, but since nobody has replied to this
particular point I will add my two cents.

LAPACK provides functions sbevd and hbevd, which compute the eigenvalues
of a banded matrix.  It also provides sbevx and hbevx, which compute
only selected eigenvalues.  The latter is almost certainly what you
want.  With a bit of research, it should be possible to figure out what
algorithm is used so it can be implemented within Eigen.

As far as I know there is still no "banded" matrix type in Eigen, so
perhaps some improvisation will be necessary to implement an API for
these algorithms.  In any event, I'd suggest making these methods part
of the public API, as people may wish to diagonalize a banded matrix

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