# hwB16 - ENEE 241 02 HOMEWORK ASSIGNMENT 16 Due Mon 03/10...

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ENEE 241 02 * HOMEWORK ASSIGNMENT 16 Due Mon 03/10 This problem investigates the least-squares approximation of the function s ( t ) = 1 - ( t - 1) 2 1 + 4( t - 1) 2 over a discrete interval of values t using a sum of three sinusoidal functions: f 1 ( t ) = sin( πt/ 2) , f 2 ( t ) = sin(3 πt/ 2) and f 3 ( t ) = sin(5 πt/ 2) (i) (5 pts.) Take t = 0 : 0 . 25 : 1 . 00 (ﬁve points in total) and let s consist of the ﬁve corresponding values of s ( t ). Display the 5 × 3 matrix V , the inner product matrix V T V and the inner product vector V T s . ( Do this part using your calculator .) (ii) (3 pts.) Use MATLAB to solve for the optimal coeﬃcient vector c and the resulting approx- imation ˆ s = Vc . Compute the relative error || s - ˆ s || / || s || . The remaining parts should be done entirely in MATLAB. In each case, submit a printout of your code and the following results: the inner product matrix V T V , the inner product vector V T s , the optimal coeﬃcient vector c and the resulting relative error

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## This note was uploaded on 03/21/2010 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.

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hwB16 - ENEE 241 02 HOMEWORK ASSIGNMENT 16 Due Mon 03/10...

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