Newton's method.

*To*: mathgroup at smc.vnet.net*Subject*: [mg5204] Newton's method.*From*: Gandalf <Gandalf at Empire.Net>*Date*: Thu, 14 Nov 1996 02:02:08 -0500*Organization*: Middle Earth*Sender*: owner-wri-mathgroup at wolfram.com

Can someone provide a little help on this problem?: Suppose I wanted to write a sequence to perform the Newton inversion of a polynomial which inverts a series 1 + a(1)x + a(2)x^2+... through a particular degree. The sequence would look like the following: (* Newton's inversion of a polynomial *) guess = 1; precision = 1; While[precision < degree, precision *=2; If[precision > degree, precision = degree]; temp = iterate[poly, precision - 1]; guess = guess + guess*(1 - temp*guess); (*The Newton iteration*) guess = iterate[guess, precision -1]; ]; (* Now guess is 1 / poly through degree of 'degree' *) ---------------- iterate would be a function, iterate[f, n] that returns a polynomial f taken through degree n. This sequence effectively doubles the precision each pass through it. I'm a little stumped on how to implement the iterate funtion. Any help greatly appreciated. Thanks.