Examples

1. Revise Newton's Method from the previous unit to make it work for any function. Instead of putting the code to compute the function and its derivative in the Newton function definition, use the fcnchk function to create function handles that can then be used to compute the desired values. Or, you can write new functions and pass the name of those functions to your Newton function.

   function x_next = Newton( x_current, f_x , dx_x )
   f = fcnchk( f_x );
   dx = fcnchk( dx_x );
   x_next = x_current - f(x_current) ./ dx(x_current);

   Use your new form of Newton's method to approximate the root of

   This code fragment uses our revised Newton function to display the first seven approximations:

   disp('        Guess #0 = 1');
   x = 1;
   for n = 1:7
       x = Newton( x, 'x^2-2', '2*x' );
       disp([ 'Approximation #' num2str(n) ' = ' num2str(x,25) ]);
   end

   Here's a transcript of the results of executing the above code fragment.

           Guess #0 = 1
   Approximation #1 = 1.5
   Approximation #2 = 1.4166666666666667
   Approximation #3 = 1.4142156862745099
   Approximation #4 = 1.4142135623746899
   Approximation #5 = 1.4142135623730951
   Approximation #6 = 1.4142135623730949
   Approximation #7 = 1.4142135623730951