sol_hw7 - CE 335 Solutions to Homework 7 1) (a) Order 1:...

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CE 335 Solutions to Homework 7 1) (a) Order 1: choose the 2 closest points to x = 3.4, 3 and 4 f 1 (x) = 6.5 - 4.5(x - 3) [applying Equation 15.18] f 1 (3.4) = 6.5 - (4.5)(0.4) = 4.7 Order 2: choose the 3 closest points: 2.5, 3, 4 f 2 (x) = 6.5 - 4.5(x - 3) - (7/3)(x - 3)(x - 4) f 2 (3.4) = f1(3.4) - (7/3)(0.4)(-0.6) = 5.26 Order 3: choose the 2 closest points on each side: 2.5, 3, 4, 5 f 3 (x) = 6.5 - 4.5(x - 3) - (7/3)(x - 3)(x - 4) + (43/30)(x - 2.5)(x - 3)(x - 4) f 3 (3.4) = f2(3.4) + (43/30)(0.9)(0.4)(-0.6) = 3481/625 or 5.57 (b) The polynomials through given points [and hence their values at 3.4] will be the same, they will only be given in different forms: Order 1: f 1 (x) = 2(x - 3) - 6.5(x - 4) Order 2: f 2 (x) = (4/3)(x - 2.5)(x - 3) - 13(x - 2.5)(x - 4) + (28/3)(x - 3)(x - 4) Order 3: f 3 (x) = 0(x - 2.5)(x - 3)(x - 4) - (4/3)(x - 2.5)(x - 3)(x - 5) + 6.5(x - 2.5)(x - 4)(x - 5) - (56/15)(x - 3)(x - 4)(x - 5) 9) i = [-2 -1 -0.5 0.5 1 2]; V = [-637 -96.5 -20.5 20.5 96.5 637];
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This note was uploaded on 08/30/2011 for the course CGN 3350 taught by Professor Lybas during the Spring '11 term at University of Florida.

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sol_hw7 - CE 335 Solutions to Homework 7 1) (a) Order 1:...

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