Re: Root Finder 12

From: Proginoskes (proginoskes_at_email.msn.com)
Date: 11/28/04 

Date: 28 Nov 2004 15:43:51 -0800

"Jon G." <jon8338@peoplepc.com> wrote in message news:<spUpd.5288$Ua.3355@newsread3.news.atl.earthlink.net>...
> You people are savage, and there's no call for it. I suppose
> you are one of the anal perfectionist obsessed with keeping on
> course down to the Angstrom to offset the Gudermanian.
>
> Newton's Method is an invention of genius. Why not use it?
> Newton just didn't come up with the approximations to plug into
> it...
>
> or did he?

No, but they have been done, and in mathematics, it doesn't matter who
does it, just that it is true and can be used.

Remember, and you have been told this repeatedly:
YOU ARE NOT ALLOWED TO USE APPROXIMATIONS.

You also say that Newton's method is great. However, there are established
results saying where a "good place" is to start. So what you have done
here is not new, and what you claim to do (to FIND roots, not just
approximate them) is FUNDAMENTALLY flawed.

The reason that Root Finder N will be wrong for all values of N is that
you have a bunch of equations of the form
t^n = A_n
t^(n-1) = A_(n-1)
t^(n-2) = A_(n-2)
etc.

Now, if you can find a value of t that satisfies ALL equations
SIMULTANEOUSLY, then you indeed have found a root of the original polynomial.
However, if there is no solution, your claim that you have found a root
is not automatic; it may be a root, or it may not. In fact, you may also
be close to a root. But this is like firing a bullet at a wall, then drawing
the target around it.
     -- Christopher Heckman

P.S. I can use "cut and paste", too.
> C. Bond wrote:
>
> > Jon G. wrote:
> >
> > [snip]
> >
> > I thought you already posted the last word on this subject. Are you
> > suffering from some kind of attention deficit disorder, or are you
> > being deliberately misleading? If there's a third possibility, I'd
> > welcome your explanation.
> >
> > --
> > There are two things you must never attempt to prove: the unprovable
> > -- and the obvious.
> > --
> > Democracy: The triumph of popularity over principle.
> > --
> > http://www.crbond.com
> >
> >

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