Is there cases where interpolation is impossible?

Question

I just learned interpolation and have been looking through it.

It seems like for every data set, interpolation is possible -- is this true? Is there any cases it is not possible to use interpolation?

Any hints or help on this question will greatly help!!!

You might be interested in the Stone-Weierstrass theorem. – J. M. ain't a mathematician Nov 10 '17 at 14:08 — J. M. ain't a mathematician, Nov 10 '17 at 14:08

score 1 · Answer 1 · answered Nov 10 '17 at 14:02

1

Consider the data set $x_0 = 0$, $y_0 = 0$, $x_1 = 0$, $y_1 = 1$. No function can serve as the interpolation here.

answered Nov 10 '17 at 14:02

Arno

score -1 · Answer 2 · answered Nov 10 '17 at 14:07

-1

Do you know the tangent function?

You have $\tan 0 = 0$ and $\tan \pi = 0$. Dare to interpolate for $\frac\pi 2$...?

answered Nov 10 '17 at 14:07

CiaPan

2 Answers2