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Problem 2 - Cubic Splines: (Problem 5.1 in ESLII) Lets consider data of the shape (X, y) with X, y E R. Consider fitting of piecewise-cubic polynomial splines to the data with continuous first and second derivatives at the two point $1 and ยง2. a) As in Lecture 7, derive the equations relating the polynomials at each boundary point. b) Show that b1(X) =1, h3(X) = X2, h5 (X) = - h2(X) = X, h4(X) = X3, h6(X) = (X - &2)3 is a basis for the cubic splines.

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