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 djmp at earthlink.net http://home.earthlink.net/~djmp/ > 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