function x=levenberg_marquardt(F,DF,x0,mu0,beta0,beta1,maxit,tol)
 
  n=length(x0);
  k=0;
  mu=mu0;
  x=x0;
  s=-(DF(x0)'*DF(x0)+mu^2*eye(n))\(DF(x0)'*F(x0));
     while norm(s)>tol && k<maxit
          [s,mu] = korrektur(F,DF,x,mu,beta0,beta1);
      x=x+s;
      k=k+1;
    end
 end