Newton-Raphson method for y=1/f(x)

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In summary, the Newton-Raphson equation for finding the solution x of the equation f(x)=0 is x = x + f'(x) / f(x). However, this equation is not applicable for finding the solution to y=1/f(x) as it will never equal 0. The Newton-Raphson method is used for approximating solutions to f(x) = 0 and cannot be used for this problem.
  • #1
Peter_F
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I need to know the Newton-Raphson equation for y=1/f(x)

I've tried to work it out, but I'm not sure if I'm right

I got this:

x = x + f'(x) / f(x)


EDIT> I've tried what I worked out and realized that it's horribly wrong.
I really need help :P



Another edit>
I don't understand why it's not working :'( I see what was wrong with what I originally got. I just made a simple mistake, but now I've got something which I'm sure is right, but won't work.

y = f(x) = 1 / g(x)

Newton Raphson:

x = x - f(x) / f'(x)
= x - (1/g(x)) / (-g'(x)/g(x)^2)
= x - g(x)^2 / -g'(x) * g(x)
= x - g(x) / -g'(x)
= x + g(x) / g'(x)

I tried this too, and it didn't work.
I'm using this in a computer program, so I need to know if I'm using the wrong equation, or if a different part of the program is messing it up.

Yet another edit> I don't need this any more. I did something different instead. Sorry for the waste of time :P
 
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  • #2
Peter_F said:
I need to know the Newton-Raphson equation for y=1/f(x)
I don't really understand the formulation of the problem. Newton-Raphson is for finding the solution x of the equation f(x)=0. What do you mean by y=1/f(x)? What is there to solve for?
 
  • #3
As krab says, the method is for approximating a solutions to f(x) = 0.

1 / f(x) will never equal 0.
 

1. What is the Newton-Raphson method for y=1/f(x)?

The Newton-Raphson method is an iterative numerical technique used to find the roots of a function. In the case of y=1/f(x), this method can be used to find the values of x that make y=0, or the points where the function crosses the x-axis.

2. How does the Newton-Raphson method work?

The method starts with an initial guess for the root, and then uses the function and its derivative to calculate a better approximation for the root. This process is repeated until the desired level of accuracy is reached.

3. What are the advantages of using the Newton-Raphson method?

The Newton-Raphson method is a fast and efficient way to find the roots of a function, especially for functions with complex or multiple roots. It also allows for a high level of accuracy, and can be used to find both real and complex roots.

4. Are there any limitations to using the Newton-Raphson method?

One limitation is that the method may fail if the initial guess is too far from the root or if the function has multiple roots close together. It also requires knowledge of the function's derivative, which may not always be readily available.

5. Can the Newton-Raphson method be used for other types of functions?

Yes, the method can be used for any type of function, not just 1/f(x). However, it is most commonly used for finding the roots of non-linear equations.

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