Numerical Analysis/Polynomial interpolation concept quiz

< Numerical Analysis

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) =
f(x) - p_n(x) =

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