RE: Newton's method

• To: mathgroup at smc.vnet.net
• Subject: [mg26281] RE: [mg26231] Newton's method
• From: "David Park" <djmp at earthlink.net>
• Date: Sun, 10 Dec 2000 00:19:53 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Derek,

I don't believe that you function has a real root. The function is complex
when x is less than about 31.8277. Above that, it starts at a real value of
about 780 and increases. You may have been mislead because the horizontal
axis in the plot is not always at y == 0, and certainly isn't for this plot.

David Park

> From: drek [mailto:drek1976 at yahoo.com]
To: mathgroup at smc.vnet.net
> Hi all,
> I am trying to use the Newton-Raphson method to find the root to an
> equation.
> The formula looks like this:
>
> newton[f_, x_, x0_, n_, opts___] :=
>   With[{df = D[f, x]}, FixedPointList[(x - f/df) /. x -> # &, N[x0], n,
> opts]]
>
> with f=Sqrt[x^2 - 2584] * Coth[0.00128 * Sqrt[x^2 - 2584]]+ Sqrt[x^2 -
> 1013].
>
> When I set
>
> newton[f, x, 31, 20]
>
> I end up getting values which do not converge. However, if I were to plot
> the function using the Plot function in Mathematica (between x
> values of 32
> and 51), it seems like the root is somewhere near 33.
>
> I would thus like to know if perhaps there is something wrong with this
> formulation for the Newton's method, or that there is some quirk
> in the Plot
> function and the function, f, in fact do not have a root at all.
>
> Thanks.
>
> Derek

```

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