diff --git a/doc/algorithms.rst b/doc/algorithms.rst index b218e61..1cfa013 100644 --- a/doc/algorithms.rst +++ b/doc/algorithms.rst @@ -7,7 +7,7 @@ Obtain bath fitting from pole fitting -------------------------------------------- In bath fitting, given :math:`\Delta(\mathrm i\nu_k)` evaluated on :math:`\{\mathrm i\nu_k\}_{k=1}^{N_{w}}`, we wish to find -:math:`V_p, E_p` such that +:math:`V_j, E_j` such that .. math:: @@ -19,19 +19,19 @@ This is achieved by the following strategy: - Find pole fitting with semidefinite constraints: -.. math:: + .. math:: \begin{equation} \Delta(\mathrm i\nu_k) = \sum_{p=1}^{N_p} \frac{M_p}{\mathrm i\nu_k - \lambda_p}, M_p\geq 0, \tag{1} \label{polefit} \end{equation} -Here :math:`M_p` are :math:`N\times N` positive semidefinite matrices. + Here :math:`M_p` are :math:`N\times N` positive semidefinite matrices. - Compute eigenvalue decomposition of :math:`M_p`: -.. math:: + .. math:: - M_p = \sum_{j=1}^{N} V_{j}^{(p)} (V_{j}^{(p)})^{\dagger}. \tag{2} \label{eigdecomp} + M_p = \sum_{j=1}^{N} V_{j}^{(p)} (V_{j}^{(p)})^{\dagger}. \tag{2} \label{eigdecomp} - Combining :math:`\eqref{polefit}` and :math:`\eqref{eigdecomp}`, we obtain the desired bath fitting: