CSE330 Assignment 02

15 Marks Deadline November 15, 2024 11:59 PM

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📄 Submission form Q1 📄 ⇒ https://forms.gle/sv8k5owt9rWuocMN7

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Question 01

  1. Consider the following table of data points/nodal points:
Time (sec) Velocity, v(t) ($ms^{-1}$)
2 10
4 20
6 25
  1. [4+1 marks] Find an interpolating polynomial of velocity that goes through the above data points by using Vandermonde Matrix method. Also compute an approximate value of acceleration at Time, t=7 sec.
  2. [4 marks] Find an interpolating polynomial of velocity that goes through the above data points by using Lagrange method.
  3. [1 mark] If a new data point is added in the above scenario, which method you should use in finding a new interpolating polynomial. Also what will be the degree of that new polynomial?

Question 02

[5 Marks] Consider the function $f(x) = 2 \cos x + 3 \sin x$. Evaluate the upper bound of the interpolation error using Cauchy’s theorem for nodes {−π/3, 0, π/3}. Keep up to 6 significant figures.