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M235A6

M235A6 - MATH 235 Least-Squares& Best Approximation...

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Unformatted text preview: MATH 235 Least-Squares & Best Approximation Assignment 6 Hand in questions 1,2,6,7,8 by 9:30 am on Wednesday November 8, 2006. 1. Find the least-squares approximation to a solution of A x = b by constructing the normal equations for ˆ x and then solving for ˆ x for the following cases: (a) A = 2 1- 2 0 2 3 , b = - 5 8 1 (b) B = 2 i- 2 2 3 i , b = 3 i 2 i 2- i Note that the normal equations over C for A x = b are A * A x = A * b . 2. You are given the data points (- 2 , 2) , (- 1 , 1) , (1 , 0) , (2 , 1). (a) Find the best linear fit to this data having the form y = β + β 1 x . (b) Find the best quadratic fit to this data having the form y = β + β 1 x + β 2 x 2 . 3. For the inconsistent linear system Ax = b where A = 1 1 1- 1 1 1- 2 1- 3 , b = 2 4 6 8 , find a least-squares solution and the corresponding least-squares error for the solution....
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M235A6 - MATH 235 Least-Squares& Best Approximation...

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