HW_7 - Homework#7 2 f1 ( x1 , x2 ) = 3 x13 + 2 x2 5 = 0 1)...

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Homework#7 1) 3 2 1 1 2 1 2 2 2 1 2 1 1 2 ( , ) 3 2 5 0 ( , ) 2 3 4 0 f x x x x f x x x x x = + - = = + + = Iteration#1 1 x =1; 2 1 x = Hence, 1 1 2 2 1 2 ( , ) 0 ( , ) 9 f x x f x x = = 2 1 1 1 1 2 2 2 1 2 1 2 1 2 9 9 4 4 4 3 7 3 3 df x dx df x dx df x x dx df x dx = = = = = + = = = J= 9 4 7 3 f= 0 9       J* x f Δ = - Using the MATLAB backslash operator, we get, x Δ = 36 81 - x=x+ x Δ = 1 1       + 36 81 - = 35 82 - Iteration#2 1 x = - 35; 2 82 x = Hence, 1 1 2 2 1 2 ( , ) 115182 ( , ) 6156 f x x f x x = - = -
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2 1 1 1 1 2 2 2 1 2 1 2 1 2 9 11025 4 328 4 3 106 3 105 df x dx df x dx df x x dx df x dx = = = = = + = = = - J= 11025 328 106 105 - f= 115182 6156 - - J* x f Δ = - Using the MATLAB backslash operator, we get, x Δ = 11.8361 46.6798 - x=x+ x Δ = 35 11.8361 82 46.6798 - + - = 23.1639 35.3202 - 2a) function [f,J] = mynonlinear(x) x1 = x(:,1); x2 = x(:,2); f1 = 3*(x1^3)+2*(x2^2)-5; f2 = 2*(x1^2)+3*(x1*x2)+4;
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This note was uploaded on 03/08/2011 for the course PGE 310 taught by Professor Klaus during the Spring '06 term at University of Texas at Austin.

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HW_7 - Homework#7 2 f1 ( x1 , x2 ) = 3 x13 + 2 x2 5 = 0 1)...

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