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The value of the function f(x) is given at n distinct values of x and its value is to be interpolated at the point x*, using all the n points. The estimate is obtained first by the Lagrange polynomial, denoted by I_L, and then by the Newton polynomial, denoted by I_N. Which one of the following statements is correct?

1. I_L is always greater than I_N
2. I_L and I_N are always equal
3. I_L is always less than I_N
4. No definite relation exists between I_L and I_N

Correct answer: I_L and I_N are always equal

Solution

Both the Lagrange polynomial and the Newton polynomial are methods of polynomial interpolation that yield the same interpolating polynomial when given the same set of data points. Therefore, their estimates at any point x* will be equal.

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