Minimal fix

JOSS/paper.md

@@ -132,7 +132,7 @@ $\gamma_k$, $\delta_{kj}$, $\eta_{jk}$, $\lambda_{kj}$ depend on the energy gap
 
 # Required input and output
 
-GX-TimeFrequency requires as input the grid size $n$, the minimal eigenvalue difference $\Delta_{\text{min}}$, and the maximal eigenvalue difference $\Delta_{\text{max}}$. For the output parameters, see Table \ref{tab:output}. The library component retrieves tabulated minimax parameters $\{\tau_j(R)\}_{j=1}^n$, $\{\sigma_j(R)\}_{j=1}^n$, $\{\omega_k(R)\}_{k=1}^n$, $\{\gamma_k(R)\}_{k=1}^n$ of the requested grid size $n$ for the smallest range $R$ that satisfies $R \ge \Delta_\text{max}/\Delta_\text{min}$. GX-TimeFrequency then rescales the retrieved minimax parameters according to Equation 6 with $\Delta_\text{min}$ and prints the results $\{\tau_j^\text{mat}\}_{j=1}^n$, $\{\sigma_j^\text{mat}\}_{j=1}^n$, $\{\omega_k^\text{mat}\}_{k=1}^n$, $\{\gamma_k^\text{mat}\}_{k=1}^n$. Fourier integration weights are computed on-the-fly via least-squares optimization. The precision of a global forward cosine transformation followed by backward cosine transformations, is measured from
+GX-TimeFrequency requires as input the grid size $n$, the minimal eigenvalue difference $\Delta_{\text{min}}$, and the maximal eigenvalue difference $\Delta_{\text{max}}$. For the output parameters, see Table \ref{tab:output}. The library component retrieves tabulated minimax parameters $\{\tau_j(R)\}_{j=1}^n$, $\{\sigma_j(R)\}_{j=1}^n$, $\{\omega_k(R)\}_{k=1}^n$, $\{\gamma_k(R)\}_{k=1}^n$ of the requested grid size $n$ for the smallest range $R$ that satisfies $R \ge \Delta_\text{max}/\Delta_\text{min}$. GX-TimeFrequency then rescales the retrieved minimax parameters according to Equation~6 with $\Delta_\text{min}$ and prints the results $\{\tau_j^\text{mat}\}_{j=1}^n$, $\{\sigma_j^\text{mat}\}_{j=1}^n$, $\{\omega_k^\text{mat}\}_{k=1}^n$, $\{\gamma_k^\text{mat}\}_{k=1}^n$. Fourier integration weights are computed on-the-fly via least-squares optimization. The precision of a global forward cosine transformation followed by backward cosine transformations, is measured from
 \fontsize{8}{10}\selectfont
 \begin{eqnarray}
 \Delta_\text{CT}=\max_{j,j'\in\{1,2,\ldots,n\}} \left| \sum_{k=1}^n \eta_{j'k} \cos(\tau_{j'}\omega_k) \cdot \delta_{kj} \cos(\omega_k\tau_j) - (\mathbb{I})_{j'j}\right|