Numerical Analysis/Polynomial interpolation concept quiz

Choose the best answer for each question:

{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?} - $$0$$ + $$1$$ - $$n$$ - $$n-1$$

{ 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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