I'm better then Newton (Method of Approximation)

In summary, the conversation discusses a Delphi program that demonstrates a more efficient method of approximation compared to the Newton-Raphson method. The program is able to beat Newton's method in terms of CPU cycles performed and can find the root in just one step under specific conditions. It is recommended to consult "Numerical Recipes in C" and to explore other programming languages beyond Delphi.
  • #1
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!
 
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  • #2
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
 
  • #3
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
 
  • #4
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.
 
  • #5
SUre, there are better methods of approximation.

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

What is the "I'm better then Newton (Method of Approximation)"?

The "I'm better then Newton (Method of Approximation)" is a mathematical method used to approximate the roots of a function. It is named after the famous scientist Sir Isaac Newton.

How does the "I'm better then Newton (Method of Approximation)" work?

This method works by using a series of approximations to get closer and closer to the actual root of a function. It uses the tangent line at a given point to estimate where the root is located.

What are the advantages of using the "I'm better then Newton (Method of Approximation)"?

The main advantage of this method is that it can quickly and accurately approximate the roots of a function. It is also relatively simple to understand and implement.

Are there any limitations to the "I'm better then Newton (Method of Approximation)"?

Yes, this method may not work for all types of functions. It also requires an initial guess for the root, which may not always be easy to determine.

How is the "I'm better then Newton (Method of Approximation)" different from other approximation methods?

This method is different from other approximation methods because it uses the derivative of the function to approximate the root. This makes it more efficient and accurate compared to other methods.

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