When dealing with 2 independent variables in vector systems :
$f_1(x,y)$ and $f_2(x,y)$, vector $F=(f_1,f_2)$ and vector $X=(x,y)$,one can derive the numerical iteration from the Newton method:
$X^{n+1}=X^{n}-J^{-1} F^{n}$ where $J = \pmatrix{df_1/dx&df_1/dy\\df_2/dx&df_2/dy}$ is the Jacobian
My question is: How to derive the same iteration expression with the Secant method? What is the expression of the Jacobian?