# hw8 - Homework#8 1(a Consider the data(1 1.1(1 1(0 0.9(0.5...

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Homework #8 1. (a) Consider the data ( - 1 , - 1 . 1) , ( - 1 , - 1) , (0 , 0 . 9) , (0 . 5 , 1 . 8) , (1 , 3 . 2) Write down the normal equations for linear least squares. (b) Solve the normal equations to get the best ﬁtting line in the least squares sense. (c) Write down the normal equations for quadratic least squares. (d) Solve the normal equations (you can use Matlab) to get the best ﬁtting parabola in the least squares sense. 2. Consider the data (0 ,y 1 ) , (0 ,y 2 ) ,..., (0 ,y n ) . Find the constant function best ﬁtting this data in the least squares sense. What is another name for this constant? 3. (a) Let f ( x ) = sin x . Approximate f 0 (1) using central diﬀerencing with h = 0 . 1, 0 . 05, 0 . 025. (b) Calculate the absolute errors E ( h ) for each of your approximations with h = 0 . 1, 0 . 05, 0 . 025. (c) Calculate E ( h ) /E ( h/ 2) for each of h = 0 . 1, 0 . 05. What value do you think this converges to as h 0? 4. (a) Consider the data x 0 0 . 1 0 . 2 0 . 3 0 . 4 f ( x ) 1 1 . 01 1 . 04 1 . 09 1 . 16 Approximate the ﬁrst derivatives of f at each of the x locations using the best of either forward, backward, or central diﬀerencing.

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## This note was uploaded on 10/17/2010 for the course MATH 174 taught by Professor Staff during the Spring '08 term at UCSD.

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hw8 - Homework#8 1(a Consider the data(1 1.1(1 1(0 0.9(0.5...

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