[SciPy-dev] Gauss-Lobatto points

[Charles R Harris]

On Mon, Sep 21, 2009 at 11:25 PM, Ondrej Certik <ondrej at certik.cz> wrote:

> On Mon, Sep 21, 2009 at 10:09 PM, Ondrej Certik <ondrej at certik.cz> wrote:
> > Hi,
> >
> > does anyone know a way to get Gauss-Lobatto points out of scipy? I
>
> P.S. Gauss-Lobatto points are the roots of
> (1-x*x)L'(x) where L(x) are Legendre
> polynomials.
>
>
If you use the (1-x*x)^.5 instead you are looking for the roots of an
associated Legendre polynomial which satisfies a recurrence that can be use
to set up a companion matrix whose eigenvalues should be the roots. The
companion matrix is multiplication by x mod
{polynomial-whose-roots-you-want}. I'm not sure what having the factor will
do, but I suspect something like that should work.

Chuck
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