20095ee103_1_hw8_sols

# 20095ee103_1_hw8_sols - L Vandenberghe EE103 Homework 8...

This preview shows pages 1–2. Sign up to view the full content.

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) ];

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 05/10/2010 for the course EE EE103 taught by Professor Jacobson during the Spring '09 term at UCLA.

### Page1 / 3

20095ee103_1_hw8_sols - L Vandenberghe EE103 Homework 8...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online