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From Axel <axel...@gmail.com>
Subject Re: Could we have a roots() method in PolynomilFunction class?
Date Sat, 28 Jun 2014 13:33:35 GMT
On Fri, Jun 27, 2014 at 10:56 PM, Thomas Neidhart
<thomas.neidhart@gmail.com> wrote:
...
> I did take a look at the stackoverflow question, and there is already a
> way to do this in Commons Math using the LaguerreSolver via the
> solveComplex and solveAllComplex methods.
>
> But it might be good to support a second way using EigenDecomposition as
> a stand-alone solver.
>
> I like the idea to add a roots() method to PolynomialFunction, but which
> method to compute the roots is more robust?

The attached link in the stackoverflow question to this paper:
http://techdigest.jhuapl.edu/TD/td2804/Williams.pdf

has this conclusion:
"We have discussed some eigenvector methods for finding the roots of multi-
variate polynomials. Unlike iterative, numerical methods typically
applied to this
problem, the methods outlined in this article possess the numerical stability of
numerical linear algebra, do not require a good initial guess of the
solution, and give all
solutions simultaneously. Furthermore, if the initial guess is poor
enough, the methods
outlined herein may converge more quickly than iterative methods."

So I think the "EigenDecomposition method" is more appropriate if you
don't have an initial guess to start from getting the roots!?

-- 
Axel Kramer

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