GATE CE 2019 Set 2 — Question 28
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Engineering Mathematics → Numerical Solution of Equations → Lagrange Interpolation
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Question
The value of the function is given at distinct values of and its value is to be interpolated at the point , using all the points. The estimate is obtained first by the Lagrange polynomial, denoted by , and then by the Newton polynomial, denoted by . Which one of the following statements is correct?
Correct answer
(B) I_L and I_N are always equal
Solution
The Uniqueness Theorem for interpolating polynomials states that for a given set of distinct data points , there exists exactly one polynomial of degree at most that passes through all these points.
Lagrange interpolation and Newton's divided difference interpolation are simply two different mathematical representations (forms) of the same unique polynomial. Since they represent the same function, their values at any point will be identical. Thus, .
Lagrange interpolation and Newton's divided difference interpolation are simply two different mathematical representations (forms) of the same unique polynomial. Since they represent the same function, their values at any point will be identical. Thus, .
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