$f:\mathbb{C}^n \to \mathbb{R}$ has Hermitian $M$ where $f(x)= x'Mx + O(\|x\|^3)$ as $x\to 0$. How might $M$ (or a representative of it) be numerically approximated?
I believe if we're handed the $\varepsilon$ where the expansion is good then entries can be approximated through some linear combination of terms like $\frac{f(x)}{\|x\|^2}$ ($x$ with small norm). Can someone provide a reference with the formula worked out, or intuition for why what I am asking for is not possible?