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

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Polynomial solver, eigenvalues of companion matrix and balancing*From*: Gael Guennebaud <gael.guennebaud@xxxxxxxxx>*Date*: Wed, 17 Mar 2010 18:26:46 +0100*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:received:in-reply-to:references :from:date:message-id:subject:to:content-type; bh=wvHOjkuJ0c0Lw6QzIqbsbn0Yjq9Ccw7FkSG1QVjRo+Q=; b=jQlt1RgrJbTeCGAf6UWAeZmCToWJbkOy2GxdgsUjyU3IkeEVoLjp8m4plVYZGDoFRI /fcxquo4SAHX5Az/E4sHgayAsbOLYjbM1t5a30xKT7PGyAbyn4TZf2aRADsDwMXzoXSw FOISlvBIQPSN+rHlal2FRbBm9+OtQ3Z0lh13g=*Domainkey-signature*: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:in-reply-to:references:from:date:message-id:subject:to :content-type; b=aMnr5uN/x1vPfAvw3iraFiD1dLE59GGzaFwuEXPrE/n1rtjWDm2NR7SEoJd0sYRN7Z xyll+8mOhdaGvBKVwRJteOhWm9IJaFxJiwIWc7ro3r1s02kLdVOkS0u0NANiXiYckzLM 75JmA69CgtHurmwbjhzN49OWF5Rr7SFKc3uqw=

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

**Follow-Ups**:**Re: [eigen] Polynomial solver, eigenvalues of companion matrix and balancing***From:*Manuel Yguel

**References**:**Re: [eigen] Polynomial solver, eigenvalues of companion matrix and balancing***From:*Manuel Yguel

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