Re: mgorth usage

[Rhys Ulerich]

> Sadly there are no usage examples nor demos and I fail to understand
> the help string.
>
> "Orthogonalize a given column vector X with respect to a given
>      orthonormal basis V using a modified Gram-Schmidt
>      orthogonalization."
>
> If V is already an orthonormal basis, how can one find an extra
> orthogonal vector?

My guess is that the "extra orthogonal vector" comes from the
"modified" in "modified Gram-Schmidt".  Gram-Schmidt is numerically
unstable.  Check out
http://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process and see if
the source code from mgorth.cc (browsable from
http://fossies.org/dox/octave-3.6.3/mgorth_8cc_source.html) matches
your expectations.

- Rhys