The levenberg-marquardt method for solving non-linear equations - algorithm

Question

I tried implement the levenberg-marquardt method for solving non-linear equations on Julia based on Numerical Optimization using the
Levenberg-Marquardt Algorithm presentation. This my code:
function get_J(ArrOfFunc,X,delta)
N = length(ArrOfFunc)
J = zeros(Float64,N,N)
for i = 1:N
for j=1:N
Temp = copy(X);
Temp[j]=Temp[j]+delta;
J[i,j] = (ArrOfFunc[i](Temp)-ArrOfFunc[i](X))/delta;
end
end
return J
end
function get_resudial(ArrOfFunc,Arg)
return map((x)->x(Arg),ArrOfFunc)
end
function lm_solve(Funcs,Init)
X = copy(Init)
delta = 0.01;
Lambda = 0.01;
Factor = 2;
J = get_J(Funcs,X,delta)
R = get_resudial(Funcs,X)
N = 5
for t = 1:N
G = J'*J+Lambda.*eye(length(X))
dC = J'*R
C = sum(R.*R)/2;
Xnew = X-(inv(G)\dC);
Rnew = get_resudial(Funcs,Xnew)
Cnew = sum(Rnew.*Rnew)/2;
if ( Cnew < C)
X = Xnew;
R = Rnew;
Lambda = Lambda/Factor;
J = get_J(Funcs,X,delta)
else
Lambda = Lambda*Factor;
end
if(maximum(abs(Rnew)) < 0.001)
return X
end
end
return X
end
function test()
ArrOfFunc = [
(X)->X[1]+X[2]-2;
(X)->X[1]-X[2]
];
X = lm_solve(ArrOfFunc,Float64[3;3])
println(X)
return X
end
But from any starting point the step not accepted. What's I doing wrong?
Any help would be appreciated.

Answer 1

I have at the moment no way to test this, but one line does not make sense mathematically:
In the computation of Xnew it should be either inv(G)*dC or G\dC, but not a mix of both. Preferably the second, since the solution of a linear system does not require the computation of the inverse matrix.
With this one wrong calculation at the center of the iteration, the trajectory of the computation is almost surely going astray.