Lecture+28--Least+Square+_+statistics+review

# Lecture+28--Least+Square+_+statistics+review - Intersection...

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» x0=[1; 1; 1]; es=1.e-6; maxit=100; » [x,f,ea,iter]=newtmult(@threesurfaces,x0) x = 1.5616 1.8113 2.8776 f = 1.0e-008 * 0.3322 0.0000 0.3322 ea = 2.0060e-008 iter = 6 initial guess Intersection of Three Surfaces

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No need to compute partial derivatives Fixed-Point Iteration Convergence Theorem ) x ,.... , x , x , x ( g x ) x ,.... , x , x , x ( g x ) x ,.... , x , x , x ( g x ) x ,.... , x , x , x ( g x 0 ) x ,.... , x , x , x ( f 0 ) x ,.... , x , x , x ( f 0 ) x ,.... , x , x , x ( f 0 ) x ,.... , x , x , x ( f n 3 2 1 n n n 3 2 1 3 3 n 3 2 1 2 2 n 3 2 1 1 1 n 3 2 1 n n 3 2 1 3 n 3 2 1 2 n 3 2 1 1 = = = = = = = = 1 K ; n K x g j i <
Example 1: Fixed-Point Solve the nonlinear system Rearrange (initial guess: x = y = z = 2 ) = + + - - = = - + + = = - + + + = 0 75 x 40 x x ) x , x , x ( f 0 50 x x 20 x ) x , x , x ( f 0 200 x x x 50 x ) x , x , x ( f 3 2 2 2 1 3 2 1 3 2 3 2 2 1 3 2 1 2 2 3 2 2 1 2 1 3 2 1 1 - + = = - - = = - - - = = /40 ) 75 x x ( ) x , x , x ( g x /20 ) x x 50 ( ) x , x , x ( g x /50 ) x x x 200 ( ) x , x , x ( g x 2 2 2 1 3 2 1 3 3 2 3 2 1 3 2 1 2 2 2 3 2 2 2 1 3 2 1 1 1

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x0=[0 0 0] n x1 x2 x3 error 0 0 0 0 1.0000 4.0000 2.5000 -1.8750 5.0760 2.0000 3.4847 1.5242 -1.3188 1.2358 3.0000 3.6759 1.8059 -1.5133 0.3921 4.0000 3.6187 1.7099 -1.4557 0.1257 5.0000 3.6372 1.7393 -1.4745 0.0395 6.0000 3.6314 1.7298 -1.4686 0.0126 7.0000 3.6333 1.7328 -1.4705 0.0040 8.0000 3.6327 1.7318 -1.4699 0.0013 9.0000
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Lecture+28--Least+Square+_+statistics+review - Intersection...

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