0
$\begingroup$

In interpolation we find a polynomial that passes through the points $x_0<x_1<\cdots<x_n$ and estimates $x\in[x_0,x_n]$, so we say the interpolation polynomial interpolates the points. But as far as I know extrapolation doesn't extrapolate but increase the accuracy of a formula that has the error term $$ M = N(h) + K_1 h + K_2 h^2 + K_3 h^3 +\cdots $$ where the $N(h)$ is our formula and $M$ is the exact solution and $K_i$'s are some constants. Why is extrapolation called extrapolation in spite of there seems be no connection between the method and its name?

$\endgroup$
1
$\begingroup$

Because you aren't familiar with enough uses of "extrapolate"? See

Interpolate: to infer values between given values

Extrapolate: to infer values outside the range of given values

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.