Science:Math Exam Resources/Courses/MATH307/April 2012/Question 01 (d)

MATH307 April 2012

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Question 01 (d)

Suppose you are given a set of N data points (xn, yn), with xn increasing, and you wish to interpolate these points with a spline function ƒ, where ƒ(x) is given by the cubic polynomial pn(x) on each interval (xn, xn+1) for n = 1, ..., N-1: $\displaystyle p_{n}(x)=a_{n}(x-x_{n})^{3}+b_{n}(x-x_{n})^{2}+c_{n}(x-x_{n})+d_{n}$ (d) Write down the matrix equation to be solved for the coefficients of the polynomials in the case N = 3, with x1 = 1, x2 = 2, x3 = 3.

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
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