\underline{G}eneralized \underline{M}inimum \underline{Res}idual,
or GMRES method is an iterative method for solving
systems of linear equations ($A x=b$) with dense matrix $A$.
-The standard GMRES\index{GMRES} is given in Algorithm~\ref{alg:GMRES}.
-It constructs a Krylov subspace\index{Krylov subspace} with order $m$,
+The standard GMRES\index{iterative method!GMRES} is given in Algorithm~\ref{alg:GMRES}.
+It constructs a Krylov subspace\index{iterative method!Krylov subspace} with order $m$,
\[ \mathcal{K}_m = \mathrm{span}( b, A^{} b, A^2 b,\ldots, A^{m-1} b ),\]
where the approximate solution $x_m$ resides.
In practice, an orthonormal basis $V_m$ that spans the
subspace $\mathcal{K}_{m}$ can be generated by
-the Arnoldi iteration\index{Arnoldi iterations}.
+the Arnoldi iterations\index{iterative method!Arnoldi iterations}.
The goal of GMRES is to search for an optimal coefficient $y$
such that the linear combination $x_m = V_m y$ will minimize
its residual $\| b-Ax_m \|_2$.
%% \end{algorithm}
\begin{algorithm}
-\caption{Standard GMRES\index{GMRES} algorithm.} \label{alg:GMRES}
+\caption{Standard GMRES\index{iterative method!GMRES} algorithm.} \label{alg:GMRES}
\KwIn{ $ A \in \mathbb{R}^{N \times N}$, $b \in \mathbb{R}^N$,
and initial guess $x_0 \in \mathbb{R}^N$}
\KwOut{ $x \in \mathbb{R}^N$: $\| b - A x\|_2 < tol$}
At each time step, SPICE\index{SPICE} has
to linearize device models, stamp matrix elements
into MNA (short for modified nodal analysis\index{modified nodal analysis, or MNA}) matrices,
-and solve circuit equations in its inner Newton iteration\index{Newton iteration}.
+and solve circuit equations in its inner Newton iteration\index{iterative method!Newton iteration}.
When convergence is attained,
circuit states are saved and then next time step begins.
This is also the time when we store the needed matrices
