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

  1. Jul 15, 2004 #1
    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 realised 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
    Last edited: Jul 16, 2004
  2. jcsd
  3. Jul 16, 2004 #2


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    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?
  4. Jul 16, 2004 #3


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    Homework Helper

    As krab says, the method is for approximating a solutions to f(x) = 0.

    1 / f(x) will never equal 0.
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