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?

$f(x)-p_{n}(x)=$