# I'm better then Newton (Method of Approximation)

• dr-dock

#### dr-dock

http://www.geocities.com/dr_physica/moa.zip

is a delphi program showing how my method of approxim outperforms/beats the Newton's one while looking for sqrt(2)

try the case A+B=2*sqrt(2) and see the magic!

There are lots of algorithms which can "beat" the Newton-Raphson method if the only criterion is the number of iterations computed. Specifically, with some domain knowledge of the kind of problem you're trying to solve, a variety of more specialized algorithms can beat Newton's method in terms of CPU cycles performed. In general, though, Newton's method is simple and works on any function with a continuously defined first derivative.

I advise that you consult "Numerical Recipes in C." I also advise that you learn a better programming language than Delphi.

- Warren

I remember last semester my math teacher would occasionally mention the Newton method. It was always funny because he'd mean to just mention it but then would get caught up in this whole discourse on how it was probably the best algorithim ever and yada yada yada and all the sudden class is up and he's done nothing but talk about how amazing Newtons algorithim was. It was quite comicall really

Originally posted by chroot
There are lots of algorithms which can "beat" the Newton-Raphson method if the only criterion is the number of iterations computed. Specifically, with some domain knowledge of the kind of problem you're trying to solve, a variety of more specialized algorithms can beat Newton's method in terms of CPU cycles performed. In general, though, Newton's method is simple and works on any function with a continuously defined first derivative.

I advise that you consult "Numerical Recipes in C." I also advise that you learn a better programming language than Delphi.

- Warren
quite right.
but the special thing is that this one is my original invention and it finds the root in just one step almost analytically under special conditions.

SUre, there are better methods of approximation.

But for the sake of approximation, I'll use the Newton-Raphson method.