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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 IL, and then by the Newton polynomial, denoted by IN. Which one of the following statements is correct?

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 IL, and then by the Newton polynomial, denoted by IN. Which one of the following statements is correct? Correct Answer I<sub>L</sub> and I<sub>N</sub> are always equal

IL and IN are always equal, since the nth degree polynomial generated by the newton’s divided difference formula is the exact same as polynomial generated by Lagrange formula.

Thus, the estimate obtained by Lagrange polynomial and Newton polynomial are equal.

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