# Thread: Linear Interpolation problem

1. ## 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 $x_1, x_2, x_3, x_4)$

2. Originally Posted by pdnhan
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