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Math Help - Newton's method

  1. #1
    Junior Member
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    Newton's method

    I dont know what they want me to do!! and I dunno how to do it!


    To solve the equation


    by Newton's Method we start with a good initial guess and then run the iteration


    until we get an approximation that is good enough for our purposes.



    Suppose you want to compute the cube root of 4 by solving the equation

    Since and Let's start with


    Then
    ,
    ,
    , and
    To check your answer compute .
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  2. #2
    Senior Member Peritus's Avatar
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    in this specific exercise f(x) = x^3 - 4
    Newton's method is an algorithm for finding the zeros of a function, you can find more information about it here:

    http://en.wikipedia.org/wiki/Newton's_method

    it's an iterative method and we need to come up with an initial guess the closer to the zero the better, in this example the Intermediate Value Theorem is used to choose the initial guess, now we have to calculate f '(x)
    f ' (x) = 3*x^2

    Xn+1 = Xn - ((Xn)^3 - 4) / (3*(Xn)^2)
    Xo = 1.5
    so:


    X1 = Xo - ((Xo)^3 - 4) / (3*(Xo)^2) = 1.5925


    X2 = X1 - ((X1)^3 - 4) / (3*(X1)^2)......
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