function y=half(func,x1,x2,varargin)
% half interval method
% y=half('poly',1.0,2.0,varargin);
  if feval(func,x1,varargin{:})*feval(func,x2,varargin{:}) > 0
    error('Invalid starting values.');
  end
  iter=0 ;
  while abs(x1-x2)/2 >= 1.0e-9
    iter=iter+1 ;
    x3=(x1+x2)/2;
    fprintf(1,'%d x3: %6.5e dx3: %2.1e \n', iter,x3,abs(x1-x2)/2);
    if feval(func,x1,varargin{:})*feval(func,x3,varargin{:}) < 0
       x2=x3;
    else
       x1=x3;
    end
  end
  y=x3;