SLQ Trace guide
To clarify that that means, here’s an abstract presentation of the generic SLQ procedure:
\begin{algorithm} \caption{Stochastic Lanczos Quadrature} \begin{algorithmic} \Input Symmetric operator ($A \in \mathbb{R}^{n \times n}$) \Require Number of queries ($n_v$), Degree of quadrature ($k$) \Function{SLQ}{$A$, $n_v$, $k$} \State $\Gamma \gets 0$ \For{$j = 1, 2, \dots, n_v$} \State $v_i \sim \mathcal{D}$ where $\mathcal{D}$ satisfies $\mathbb{E}(v v^\top) = I$ \State $T^{(j)}(\alpha, \beta)$ $\gets$ $\mathrm{Lanczos}(A,v_j,k+1)$ \State $[\Theta, Y] \gets \mathrm{eigh\_tridiag}(T^{(j)}(\alpha, \beta))$ \State $\tau_i \gets \langle e_1, y_i \rangle$ \State < Do something with the node/weight pairs $(\theta_i, \tau_i^2)$ > \EndFor \EndFunction \end{algorithmic} \end{algorithm}