Re: [Axiom-math] solving polynomial equations

[Dylan Thurston]

On Fri, Sep 10, 2004 at 03:30:53PM -0400, root wrote:
> General Solution for Polynomial Equations
> 
> http://arxiv.org/pdf/math.CA/0408264
> 
> the report is that a Dutch student found a formula to determine the
> roots of any polynomial equation. Although an exact solution has been
> proven impossible for higher orders, this is not the case for numerical
> solutions.

Summary of the thread in sci.math: 

(a) The problem is badly stated; the correct statement is that there
is no closed-form solution to the general quintic using radicals.
This is not relevant for much of anything; for instance, there are
perfectly satisfying closed-form solutions using elliptic functions,
which are quite computable.

(b) The technique in the paper is a very old technique for
approximating solutions to polynomials, which doesn't work very well.

Peace,
        Dylan

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