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Math Help - Linear Interpolation problem

  1. #1
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    Linear Interpolation problem

    Let  f(x) = x^2 - 2 , c \in [0,2] satisfying f(c) = 0
    Use Linear Interpolation to find the first 5 approximations to c (so  x_0 = 1 Find  x_1, x_2, x_3, x_4)
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by pdnhan View Post
    Let  f(x) = x^2 - 2 , c \in [0,2] satisfying f(c) = 0
    Use Linear Interpolation to find the first 5 approximations to c (so  x_0 = 1 Find  x_1, x_2, x_3, x_4)
    Well:

    let x_0=1, and x_{00}=2, so:

    f(x_0)=-1, f(x_{00})=2

    So:

    x_1=x_0-\frac{x_0-x_{00}}{f(x_0)-f(x_{00})} \; (f(x_0)-1)

    Then:

    x_1=1.33333.. and f(x_1)=-0.222222..

    So the next stage is:

    x_2=x_1-\frac{x_1-x_{00}}{f(x_1)-f(x_{00})} \; (f(x_1)-0)

    and so on (always keeping the pair of points that bracket the solution)

    CB
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