Re: [eigen] Polynomial solver, eigenvalues of companion matrix and balancing

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Great !
my username on bitbucket is the following:


- cheers


P.S. happy birthday, Benoît e-mail was really a good one ;)

On Wed, Mar 17, 2010 at 6:26 PM, Gael Guennebaud
<gael.guennebaud@xxxxxxxxx> wrote:
> You're welcome to commit a new module. Please put it in the unsupported/
> folder, and to simplify further development, I invite you to create an
> account on bitbucket so that you can directly commit your changes to this
> module. I only need your username on bitbucket to enable write accesses.
> gael.
> On Wed, Mar 17, 2010 at 4:28 PM, Manuel Yguel <manuel.yguel@xxxxxxxxx>
> wrote:
>> Hello, I come again with the qr way of polynomial solving because the
>> Bezier bissection I am working on, only provide the real roots of the
>> polynomial.
>> It is interesting per se, but somebody might want the complex roots
>> too, so the qr way is still interesting.
>> Furthermore it will provide a concurrent solver to make comparisons.
>> I have written balancing and tested the solver: the same behaviour
>> appears.
>> So I checked what is going wrong and found two things:
>> 1) the problem shows up only for floats not doubles (do you have
>> experienced any particular problem with qr + float ?)
>> 2) for doubles the problem shows up when the polynomial is not square
>> free (i.e. with roots with multiplicity) as far as I have
>> investigated.
>> Furthermore I made some comparisons with the GSL solver, which is only
>> provided for doubles (he, he ...) and the results are the same in term
>> of precision.
>> What do you think of providing the solver like that with a warning
>> raised when it is instanciated with floats ?
>> On the other hand, I am continuing working on the Bezier bissection
>> solver and the first step for this solver is to find the equivalent
>> square free polynomial (he he ^2), so I propose to provide this
>> functionality in general.
>> If you agree, I will provide a patch for that module and add to the TODO:
>> - investigate why it fails so badly on floats (and fix it if possible),
>> - provide a qr algorithm adapted to the shape of the companion matrix
>> and possibly optimized for the particular case where we do not need
>> the eigenvectors, neither the Q matrix.
>> - best regards,
>> Manuel

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