Finite-difference Jacobian
= Finite-difference Jacobian
An approximation to a <Jacobian matrix> obtained using <finite differences> instead of analytic partial derivatives. For a vector-valued function $F$, the forward-difference entry is $J_{ij}\approx(F_i(x+h e_j)-F_i(x))/h$, where $e_j$ is a coordinate <basis vector>. The step $h$ balances truncation and rounding errors; the resulting matrix can be used in a <Newton root-finding iteration>.