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%   Dichotomous Search for Minimizer of a Unimodal Function  %
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%
 A=[];C=[];
%%
%%   Select Parameters: endpoints & error tolerance
 x_l = 0 , x_r = 2 , eps= .001, eps_1 = eps/2;
%
%%   Initialize variables
 a= x_l; b = x_r; N = round( log(eps_1/(b-a))/log(.5+2*eps_1)) ,
 F = min(phi(a),phi(b))
%%
%%   Begin interation loop
 for i=1:N;
  mid = (a+b)/2;
  a1 = mid;       b1 = mid + eps_1;
  % build array to show subinterval selections
  C=[ C
      [a a1 b1 b] ];
  F1 = phi(a1);   F2 = phi(b1);
  if F1 < F2,               %%  select LEFT subinterval
      b = b1 ; F= min(F,F1);
     else,                  %%  select RIGHT subinterval
      a = a1 ; F=min(F,F2);
     end
 % build array of interval [a,b] and current Min of phi
  A=[ A
      [a b F] ];
  end
C
A