# Linear Interpolation problem

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• Oct 4th 2009, 09:41 PM
pdnhan
Linear Interpolation problem
Let $\displaystyle f(x) = x^2 - 2 , c \in [0,2]$ satisfying f(c) = 0
Use Linear Interpolation to find the first 5 approximations to c (so $\displaystyle x_0 = 1$ Find $\displaystyle x_1, x_2, x_3, x_4)$
• Oct 4th 2009, 10:41 PM
CaptainBlack
Quote:

Originally Posted by pdnhan
Let $\displaystyle f(x) = x^2 - 2 , c \in [0,2]$ satisfying f(c) = 0
Use Linear Interpolation to find the first 5 approximations to c (so $\displaystyle x_0 = 1$ Find $\displaystyle x_1, x_2, x_3, x_4)$

Well:

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

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

So:

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

Then:

$\displaystyle x_1=1.33333..$ and $\displaystyle f(x_1)=-0.222222..$

So the next stage is:

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

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

CB