[SciPy-dev] Gauss-Lobatto points
Ondrej Certik
ondrej@certik...
Tue Sep 22 12:04:26 CDT 2009
Hi Chuck!
On Tue, Sep 22, 2009 at 6:51 AM, Charles R Harris
<charlesr.harris@gmail.com> wrote:
>
>
> On Mon, Sep 21, 2009 at 11:25 PM, Ondrej Certik <ondrej@certik.cz> wrote:
>>
>> On Mon, Sep 21, 2009 at 10:09 PM, Ondrej Certik <ondrej@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.
Thanks for the help!
Ondrej
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