function r=iqi(f,x1,x2,x3,varargin)
%IQI Root finding, inverse quadratic interpolation method.
%   X=IQI(F,X1,X2,X3) attempts to find the solution of F(X)=0 given initial
%   guesses X1, X2 and X3 using the inverse quadratic interpolation method. 
%   F is a function handle.
%
%   X=IQI(F,X1,X2,X3,P1,P2,...) passes the parameters P1,P2,... to F.
%
%   See also NEWTON, BISECTION, SECANT.

%   Francisco J. Beron-Vera
%   $Revision: 1.1 $  $Date: 2006/09/19 13:28:03 $

N=25;
x=zeros(1,N);
x(1:3)=[x1 x2 x3];
n=0;
while abs(x(n+3)-x(n+2))>eps*abs(x(n+3))
   n=n+1;
   if n>N
      warning('Tolerance not satisfied.')
      break
   end
   a=f(x(n),varargin{:})/f(x(n+1),varargin{:});
   b=f(x(n+2),varargin{:})/f(x(n+1),varargin{:});
   c=f(x(n+2),varargin{:})/f(x(n),varargin{:});
   x(n+3)=...
      x(n+2)-...
      (b*(b-a)*(x(n+2)-x(n+1))+(1-b)*c*(x(n+2)-x(n)))/...
      ((a-1)*(b-1)*(c-1));
end
r=x(n+3)