# Numerical Analysis/Polynomial interpolation concept quiz

Choose the best answer for each question:

1 Of the following polynomial interpolation methods, which is generally considered the method of choice due to its relative ease of use?

 Vandermonde matrix Lagrange method Newton form

2 Which method is the best choice when the desired degree of the interpolating polynomial is known?

 Vandermonde matrix Lagrange method Newton form

3 Which method is best suited when the desired degree of the interpolating polynomial is unknown?

 Vandermonde matrix Lagrange method Newton form

4 Which method is best suited to the addition of points to the data set?

 Vandermonde matrix Lagrange method Newton form

5 What is the computational cost of finding an interpolating polynomial through $n$ points using the Newton form?

 $O(n)$ $O(n^{2})$ $O(n^{3})$ $O(n^{4})$ 6 What is the computational cost of the Vandermonde method, using Gaussian elimination?

 $O(n)$ $O(n^{2})$ $O(n^{3})$ $O(n^{4})$ 7 Under what conditions can the Lagrange method of polynomial interpolation fail?

 When $n>10$ . When $n$ is not a perfect square. When two or more of your $y$ -values are equal. The Lagrange method cannot fail.

8 Given a set of $n$ points, exactly how many interpolating polynomials can be found to pass through the points?

 $0$ $1$ $n$ $n-1$ 9

 What is the error term of an interpolation polynomial? $f(x)-p_{n}(x)=$ 