  This work investigates the asymptotic behaviour of the gradient approximation
method called the generalized simplex gradient (GSG). This method has an error
bound that at first glance seems to tend to infinity as the number of sample
points increases, but with some careful construction, we show that this is not
the case. For functions in finite dimensions, we present two new error bounds
ad infinitum depending on the position of the reference point. The error bounds
are not a function of the number of sample points and thus remain finite.
