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GATE 2019 CE (CE2) – Question 28

Engineering Mathematics · Numerical Methods: Error analysis, algebraic equations, interpolation, differentiation, integration, ODEs · 1 mark · Multiple choice

A function is known at n distinct abscissae and is interpolated at $x^*$ using all n points. Lagrange and Newton interpolation estimates are $I_L$ and $I_N$. Which 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 $I_N$.

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Show answer and explanation

Correct answer: (B) $I_L$ and $I_N$ are always equal.

Explanation

There is one polynomial of degree at most n − 1 interpolating n distinct abscissae. Newton and Lagrange forms represent that same polynomial; hence **IL = IN, B**, apart from numerical roundoff. The appended key row is blank, so polynomial uniqueness establishes the answer independently.