Exercise 2Quadratic spline [40pts]. Consider a set of points (xi.y)-0. N of your

Question

Exercise 2Quadratic spline [40pts]. Consider a set of points (xi.y)-0. N of your choice with N > 4. All y coordinates should be positive. Moreoever, they should neither belong to a straight line nor to a quadratic curve. It is asked to find a quadratic spline y(x) (every branch of the spline is a quadratic polynomial) interpolating these points. 1. Explain how many conditions are missing to enforce uniqueness. 2. Find a spline which minimizes its length. 3. Find a spline which minimizes the area under the curve. 4. Plot the found splines on the same figure.

Explanation / Answer

{ 0, 1, 2, 3, 4}; y = {1, .5, .2, .1, (1/17)}; n = Length[t]; z = y; z[[0]] = 0; For[i = 2, i

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