# 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 ${\displaystyle n}$ points using the Newton form?

 ${\displaystyle O(n)}$ ${\displaystyle O(n^{2})}$ ${\displaystyle O(n^{3})}$ ${\displaystyle O(n^{4})}$

6 What is the computational cost of the Vandermonde method, using Gaussian elimination?

 ${\displaystyle O(n)}$ ${\displaystyle O(n^{2})}$ ${\displaystyle O(n^{3})}$ ${\displaystyle O(n^{4})}$

7 Under what conditions can the Lagrange method of polynomial interpolation fail?

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

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

 ${\displaystyle 0}$ ${\displaystyle 1}$ ${\displaystyle n}$ ${\displaystyle n-1}$

9

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