Numerical Analysis/Polynomial interpolation concept quiz

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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 points using the Newton form?

6

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

7

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

When .
When is not a perfect square.
When two or more of your -values are equal.
The Lagrange method cannot fail.

8

Given a set of points, exactly how many interpolating polynomials can be found to pass through the points?

9

What is the error term of an interpolation polynomial?