"$$D^{-1} = \\mathcal F^\\dagger S_h^{-1}\\mathcal F + R^\\dagger N^{-1} R.$$\n",
"In the end, we want to apply $D$ to $j$, i.e. we need the inverse action of $D^{-1}$. This is done numerically (algorithm: *Conjugate Gradient*). \n",
"\n",
"- One can define the *condition number* of a non-singular and normal matrix $A$:\n",
"where $\\lambda_{\\text{max}}$ and $\\lambda_{\\text{min}}$ are the largest and smallest eigenvalue of $A$, respectively.\n",
"\n",
"- The larger $\\kappa$ the slower Conjugate Gradient.\n",
"\n",
"- By default, conjugate gradient solves: $D^{-1} m = j$ for $m$, where $D^{-1}$ can be bad conditioned. If one knows a non-singular matrix $T$ for which $TD^{-1}$ is better conditioned, one can solve the equivalent problem:\n",
"$$\\tilde A m = \\tilde j,$$\n",
"where $\\tilde A = T D^{-1}$ and $\\tilde j = Tj$.\n",
"\n",
"- In our case $S^{-1}$ is responsible for the bad conditioning of $D$ depending on the chosen power spectrum. Thus, we choose\n",
