Science:Math Exam Resources/Courses/MATH307/April 2012/Question 05 (a)

MATH307 April 2012

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Question 05 (a)
You are given a set of 100 data points (xn, yn) with xn increasing. (a) Suppose you wish to use Lagrange interpolation to interpolate the data points. What degree of polynomial would you use and why?

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint

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Solution
Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. When using Lagrange interpolation, we choose to fit the point with a polynomial of lowest degree that goes through all the points. We have 100 points, meaning that we need a 99 degree polynomial: $p(x)=a_{1}x^{99}+a_{2}x^{98}+...+a_{99}x+a_{100}$

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