%
% Written by:
% --
% John L. Weatherwax                2009-04-21
%
% email: wax@alum.mit.edu
%
% Please send comments and especially bug reports to the
% above email address.
%
%-----

close all; clc; clear all; 

% EPage 136

xs = 20:2:30;
ys = xs.^1.4 - sqrt(xs) + 1./xs - 100;

% Find an interval that brackets our root graphically
plot( xs, ys, '-' ); 
grid on; 

% find the value of x such that aitken( xs, ys, x ) ~ 0 use aitken with a bisection like algorithm 
%
xl = 27; fl = aitken( xs, ys, xl );
xr = 28; fr = aitken( xs, ys, xr );
assert( fl*fr < 0 );
while (xr-xl)>1.e-4 
  xm = 0.5 * ( xl + xr );
  fm = aitken( xs, ys, xm );
  if fm*fl > 0 
    fl = fm;
    xl = xm;
  else
    fr = fm;
    xr = xm;
  end
end
0.5 * ( xl + xr ) % print our root