2. Numerical Methods

Approximation Theory — Quiz

Test your understanding of approximation theory with 5 practice questions.

Practice Questions

Question 1

Under what condition on the matrix $A$ does the ordinary least squares problem $\min_x\|Ax-b\|_2$ have a unique solution?

Question 2

What is the geometric interpretation of the least squares solution $x$ to $Ax\approx b$?

Question 3

Which statement best describes the primary difference between polynomial interpolation and least squares approximation?

Question 4

Using Horner’s method, how many multiplications are required to evaluate a degree-$n$ polynomial at a single point?

Question 5

Which distribution of interpolation nodes on $[-1,1]$ helps mitigate Runge’s phenomenon when approximating functions with polynomials?