Approximating Hilbert norm of a function

Question

Let's assume that I have a function $f \in \mathcal{H}$, where RKHS $\mathcal{H}$ is induced by kernel $\kappa$. If I can evaluate $f$ in any point, how I can approximate $||f||^2_\mathcal{H}$? I have a suspicion that I can use $\mathbf{f}^{\top}K^{-1}\mathbf{f}$ where $\mathbf{f}$ is a vector of evaluations of $f$ at some grid $X$, and $K$ is a Gramm matrix. I've managed to show that $\mathbf{f}^{\top}K^{-1}\mathbf{f}$ is a lower bound of the norm, but I can not show that $$ \mathbf{f}^{\top}K^{-1}\mathbf{f} \xrightarrow[]{n \to \infty} ||f||^2_{\mathcal{H}} $$ where $n$ is a number of points in the grid.