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Topic: Newton's method.
Replies: 1   Last Post: Nov 12, 1996 1:22 PM

 Messages: [ Previous | Next ]
 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.

Date Subject Author
11/9/96 Gandalf
11/12/96 Daniel Lichtblau