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Math Help - Establish formula for approximation

  1. #1
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    Establish formula for approximation

    If x=a is an approximation for the equation f(x)=0, then x=a-\frac{f(a)}{f'(a)} is a closer approximation, establish the formula
    x_{r+1}=x_r (2-Nx_r) as a method of successive approximations to the reciprocal of N.

    I don't know where to begin.
    Thank you
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  2. #2
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    As an iterative formula, Newton's method takes the form,

    \displaystyle x_{n+1}=x_{n}-\frac{f(x_{n})}{f^{\prime}(x_{n})}.

    To use the method to find the reciprocal of the number N, you have to solve the equation

    \displaystyle \frac{1}{x}-N=0,

    in which case

    \displaystyle f(x)= \frac{1}{x}-N.

    Substitute this into the RHS of the formula and simplify.
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  3. #3
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    how did you arrive at the \frac{1}{x}-N=0?
    can you give me like the reason, logic behind it?
    thanks!
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  4. #4
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    Quote Originally Posted by arze View Post
    how did you arrive at the \frac{1}{x}-N=0?
    can you give me like the reason, logic behind it?
    thanks!
    If x=1/N, then 1/x-N=0.
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