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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?
(A) $I_{L}$ is always greater than $I_{N}$
(B) $I_{L}$ and $I_{N}$ are always equal
(C) $I_{L}$ is always less than $I_{N}$
(D) No definite relation exists between $I_{L}$ and $I_{N}$


Question ID - 157052 | Toppr Answer

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?
(A) $I_{L}$ is always greater than $I_{N}$
(B) $I_{L}$ and $I_{N}$ are always equal
(C) $I_{L}$ is always less than $I_{N}$
(D) No definite relation exists between $I_{L}$ and $I_{N}$

1 Answer - 5876 Votes

3537

Answer Key : (B) -

$I_{L}$ and $I_{N}$ are always equal



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