function z = Broyden(fcn,x,tol)
% Broyden method for the roots of 
% a set of nonlinear equations
% Requires no explicit computation of Jacobian
% fcn = string containing the name of the function (vector)
% x = an initial guess (vector)
% tol = the tolerance
% Usage z = Broyden('fcnEg5p15',[1; 2],1e-12)
% See example 5.16 on p.242 of Heath
% This version requires only O(n^2) arithmetic operations/loop.
% K. Ming Leung, 02/21/03

maxIt = 20;
it = 0; err = 1;
A=eye(length(x));
% Replace the above line by the following line
% if a function to compute the Jacobian is available.
%B = feval('fcnJEg5p15',x); A=inv(B);

f = feval(fcn,x);
s = -A*f;     % Change in the root 
n2 = s.'*s;   % Norm squared
x = x+s;      % Next approximation to the root
while it < maxIt & sqrt(n2) > tol
    f = feval(fcn,x);
    u = A*f;
    v = s.'*A;
    d = 1/(n2+s.'*u);
    A = A-d*u*v;
    s = -A*f;
    n2 = s.'*s;
    x = x+s,
    it = it+1;
end
z = x;




