2. Numerical Methods

Interpolation — Quiz

Test your understanding of interpolation with 5 practice questions.

Practice Questions

Question 1

What formula defines the j-th Lagrange basis polynomial $\ell_j(x)$ in polynomial interpolation?

Question 2

What is the expression for the interpolation error term $R_n(x)$ when interpolating a function $f$ at nodes $x_0,\dots,x_n$?

Question 3

Which choice of interpolation nodes on $[-1,1]$ minimizes the maximum of $\left|\prod_{i=0}^n(x-x_i)\right|$ and thus reduces Runge oscillations?

Question 4

In polynomial interpolation via the monomial basis, the Vandermonde matrix $V$ has entries $V_{ij}$ equal to what?

Question 5

A cubic spline interpolation of data ensures continuity of which derivatives at each interior knot?