20095ee103_1_hw8_sols

20095ee103_1_hw8_sols - L Vandenberghe EE103 Homework 8...

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L. Vandenberghe 12/3/09 EE103 Homework 8 solutions 1. We are interested in minimizing g ( x ) = m s i =1 r i ( x ) 2 x = ( u c , v c , R ) and where r i ( x ) = ( u i x 1 ) 2 + ( v i x 2 ) 2 x 2 3 . At iteration k of the Gauss-Newton method we solve the least-squares problem minimize b A ( k ) x b ( k ) b 2 with A ( k ) = r 1 ( x ( k ) ) T r 2 ( x ( k ) ) T . . . r m ( x ( k ) ) T = 2 x ( k ) 1 u 1 x ( k ) 2 v 1 x ( k ) 3 x ( k ) 1 u 2 x ( k ) 2 v 2 x ( k ) 3 . . . . . . . . . x ( k ) 1 u m x ( k ) 2 v m x ( k ) 3 , and b ( k ) = Ax ( k ) r ( x ( k ) ). The Fgure on the next page is produced by the following Matlab code. [u, v] = ch14ex6; m = length(u); uc = -2; vc = 6; R = 1; x = [uc; vc; R]; for k = 1:50 r = (u - x(1)).^2 + (v - x(2)).^2 - x(3)^2; A = 2 * [ x(1) - u, x(2) - v, -x(3)*ones(m,1) ];
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This note was uploaded on 05/10/2010 for the course EE EE103 taught by Professor Jacobson during the Spring '09 term at UCLA.

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20095ee103_1_hw8_sols - L Vandenberghe EE103 Homework 8...

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