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Math Help - Newton's Method: Numerical Analysis

  1. #1
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    Newton's Method: Numerical Analysis

    Could someone please so me how Newton's Method is used in Numerical Analysis? My teacher is doing a horrible job of teaching it and he skips a lot of steps.

    Newtons Method:

    X(n+1) = x(n) - f(x(n))/f'(x(n)) (n) is a subcript to x.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Dream View Post
    Could someone please so me how Newton's Method is used in Numerical Analysis? My teacher is doing a horrible job of teaching it and he skips a lot of steps.

    Newtons Method:

    X(n+1) = x(n) - f(x(n))/f'(x(n)) (n) is a subcript to x.
    It is a method to find the solutions to a function using the derivative and the original function only

    For example consider x^4-3x^3+17\sin(x)=0

    We have to make an initial guess..lets say 2

    So we set up our first iteration

    x_1=2-\frac{(2)^4-3(2)^4+17\sin(2)}{4(2)^2-9(2)^2+17\cos(2)}=\psi

    C is just because I dont have my calculator

    So then

    x_2=\psi-\frac{\psi^4-3\psi^4+17\sin(\psi))}{4\psi^3-9\psi^2+17\cos(\psi)}

    and then obviously

    x_n=\psi_n-\frac{\psi_n^4-3\psi_n^3+17\sin(\psi_n)}{4\psi_n^3-9\psi_n^2+17\cos(\psi_n)}

    and as n\to\infty the iterations will yield that zero of th function
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  3. #3
    MHF Contributor arbolis's Avatar
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  4. #4
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    Thanks guys. Newton's Method seems to be very simple to understand. It just was my teacher, who cann't really teach but he knows his stuff. Mainly I see that you can manipulate problems in many ways to get your desired outcome.
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