Computer-oriented approaches to pattern recognition

Product Details

• Series: Mathematics in Science and Engineering (Book 83)
• Hardcover: 250 pages
• Publisher: Academic Press (June 11, 1972)
• Language: English
• ISBN-10: 012488850X
• ISBN-13: 978-0124888500
• Product Dimensions: 9.2 x 6.2 x 0.9 inches
  

1. t = linspace(0,3);
   
2. y = (2-t.^2).^2;
   
3. figure; plot( t, y, '-o' );
   
4. 
   
5. disp( 'Truth is:' );
   
6. sqrt(2)
   
7. 
   
8. % A:
   
9. x(1) = 1.5;
   
10. for i=2:5,
    
11.   x(i) = x(i-1) + 4*(0.1/(i-1))*x(i-1)*(2-x(i-1)^2);
    
12. end
    
13. x
    
14. 
    
15. % B:
    
16. x(1) = 1.5;
    
17. for i=2:5,
    
18.   x(i) = x(i-1) + 4*(0.1)*x(i-1)*(2-x(i-1)^2);
    
19. end
    
20. x
    
21. 
    
22. % C:
    
23. x(1) = 1.5;
    
24. for i=2:5,
    
25.   x(i) = x(i-1) + 4*x(i-1)*(2-x(i-1)^2);
    
26. end
    
27. x

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1. function prob_3_2
   
2.   
   
3. close all;  
   
4. 
   
5. t = linspace(0,3);
   
6. y = abs(2-t.^2);
   
7. figure; plot( t, y, '-o' );
   
8. 
   
9. disp( 'Truth is:' );
   
10. sqrt(2)
    
11. 
    
12. nIters = 100;
    
13. epsilon = 0.05;
    
14. x(1) = 1.5;
    
15. for i=2:nIters,
    
16.   x(i) = x(i-1) - epsilon*fPrime(x(i-1));
    
17. end
    
18. x
    
19. 
    
20. figure; plot( x, 'or' );
    
21. 
    
22. function fp = fPrime( x )
    
23. 
    
24. if( x < -sqrt(2) )
    
25.   fp = 2*x;
    
26. elseif( x > +sqrt(2) )
    
27.   fp = 2*x;
    
28. else
    
29.   fp = -2*x;
    
30. end

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1. function prob_3_3
   
2.   
   
3. close all;  
   
4. 
   
5. Y = [ 0 1 1;
   
6.       1 0 -1;
   
7.       1 1 1;
   
8.       2 0 -1];
   
9. w0 = [ 1 1 1 ];
   
10. 
    
11. nIters = 50;
    
12. w(1,:) = w0;
    
13. for i=2:nIters,
    
14.   tmp1 = Y*(w(i-1,:)')-ones(4,1);
    
15.   f  = mean( tmp1.^2 );
    
16.   gf(1) = 0.5*( tmp1' * Y(:,1) );
    
17.   gf(2) = 0.5*( tmp1' * Y(:,2) );
    
18.   gf(3) = 0.5*( tmp1' * Y(:,3) );
    
19.   gfNorm = norm( gf );
    
20.   w(i,:) = w(i-1,:) - (1/gfNorm)*gf;
    
21. end
    
22. w
    
23. 
    
24. figure; imagesc( w ); colorbar;

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