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;
(* 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.