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Gandalf
Posts:
1
Registered:
12/7/04


Newton's method.
Posted:
Nov 9, 1996 1:55 AM


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.



