5. Interpolation II

Interpolation Error — Quiz

Test your understanding of interpolation error with 5 practice questions.

Practice Questions

Question 1

If $p(x)$ interpolates $f(x)$, which expression gives the interpolation error at $x$ when the error is defined as the true value minus the interpolant?

Question 2

At each interpolation node $x_i$, what is the interpolation error?

Question 3

In the standard remainder term for interpolation by a degree $n$ polynomial, what is the order of the derivative of $f$ that appears?

Question 4

If $f(x)$ is already a polynomial of degree at most $n$, and $p_n(x)$ is the degree $n$ interpolating polynomial, what is the interpolation error?

Question 5

For linear interpolation on $[a,b]$, the error term contains the factor $(x-a)(x-b)$. What does this factor tell you about the error at the endpoints?