20095ee103_1_hw8

20095ee103_1_hw8 - L Vandenberghe EE103 Fall 2009 Homework...

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L. Vandenberghe EE103 Fall 2009 Homework 8 Due Thursday 12/3/09. 1. Exercise 14.6. We solve a specifc instance o± the problem in exercise 14.6. Download the fle ch14ex6.m ±rom the course website, and execute the Matlab command [u, v] = ch14ex6; to generate the data in the fgure on page 211. The commands plot(u, v, ’o’); axis square will create a plot o± the m = 50 points ( u i , v i ) in the fgure. Apply the Gauss-Newton method to the nonlinear least-squares problem minimize g ( u c , v c , R ) = m i =1 (( u i u c ) 2 + ( v i v c ) 2 R 2 ) 2 . The variables are u c , v c , R . Terminate the iteration when b∇ g ( u c , v c , R ) b ≤ 10 - 5 . You can select a good starting point ±rom the plot o± the 50 points ( u i , v i ). With a good starting point, no backtracking line search will be needed, so you can ±ollow the outline
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