Numerical Analysis/Polynomial interpolation concept quiz

Choose the best answer for each question:

<quiz display=simple> {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

{Which method is the best choice when the desired degree of the interpolating polynomial is known?} - Vandermonde matrix + Lagrange method - Newton form

{Which method is best suited when the desired degree of the interpolating polynomial is unknown?} - Vandermonde matrix - Lagrange method + Newton form

{Which method is best suited to the addition of points to the data set?} - Vandermonde matrix - Lagrange method + Newton form

{What is the computational cost of finding an interpolating polynomial through $n$ points using the Newton form?} - $O(n)$ + $O(n^2)$ - $O(n^3)$ - $O(n^4)$

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

{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.

{Given a set of $n$ points, exactly how many interpolating polynomials can be found to pass through the points?} - $0$ + $1$ - $n$ - $n-1$

{ |type="{}"} What is the error term of an interpolation polynomial?
$f(x)-p_n(x)=$ { $\frac{f^{(n+1)}(\xi )}{(n+1)!}\prod _{i=0}^n(x-x_i)$ }

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