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Home Tools assignment-5.pdf x assignment-4.pdf Sustainable and... Presentation title... Kincaid D , Chene... Sign In W CP T 1 12 193% 40 Share Exercise 22 [3 + 4 + 4 + 4 Points]: Consider B-splines over the nodes ui E {0, 1, 2, 3, 4}. Po a) Draw the B-splines No (u), No (u), and No (u). b) Use your construction from a) to estimate No (0), No (1), No (2), and No (3). Explain your result. Note that there is no need to actually derive and evaluate the recursive formula for any u. c) Using part b), derive the collocation matrix for spline interpolation at the nodes 2, 3, ..., n + 1 with the spline s(u) = Zio siN? (u) defined over the node set {0, 1, 2, . .., n + 2). d) Solve the interpolation problem when assuming nodes 2, 3, 4 and the values 3, 2, 5. Provide the interpolating spline s(u) and sketch it. Exercise 23 [not graded, w/o Points]: Given a spline b(u) = E-obi N? (u) in B-spline representation over the nodes {0, 1, 3, 4, 7}. a) Derive the B-splines N? (u) for i = 0, 1 in piecewise monomial form for the given nodes. b) Consider bi = i + 1 for i = 0, 1 and derive the spline b(u) in piecewise monomial form. c) Evaluate b(u) at all the nodes and sketch the spline. i.e. E Nr (u) = 1. Exercise 24 [not graded, w/o Points]: Show that the B-splines fulfill the partition of unity property