function J = JacobianF(x)
% this function is used in solving an example of
% a system of non-linear equations
   n = length(x);
   d = -4*x + 3*ones(n,1); D = sparse(1:n,1:n,d,n,n);
   c = -2*ones(n-1,1); C = sparse(1:n-1,2:n,c,n,n);
   e = -ones(n-1,1); E = sparse(2:n,1:n-1,e,n,n);
   J = C + D + E;
end