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authorJaron Kent-Dobias <jaron@kent-dobias.com>2022-09-02 14:39:23 +0200
committerJaron Kent-Dobias <jaron@kent-dobias.com>2022-09-02 14:39:23 +0200
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Fixed some wording in FRSB section.arxiv-v2
Diffstat (limited to 'frsb_kac-rice.tex')
-rw-r--r--frsb_kac-rice.tex8
1 files changed, 4 insertions, 4 deletions
diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex
index 7b6575c..875d5a9 100644
--- a/frsb_kac-rice.tex
+++ b/frsb_kac-rice.tex
@@ -724,9 +724,9 @@ sufficiently close to the correct answer. This is the strategy we use in
\label{sec:frsb}
This reasoning applies equally well to FRSB systems. In the end, when the
-limit of $n\to0$ is taken, each can be represented in the canonical way by its
-diagonal and a continuous function on the domain $[0,1]$ which parameterizes
-each of its rows, with
+limit of $n\to0$ is taken, each matrix field can be represented in the
+canonical way by its diagonal and a continuous function on the domain $[0,1]$
+which parameterizes each of its rows, with
\begin{align}
C\;\leftrightarrow\;[c_d, c(x)]
&&
@@ -735,7 +735,7 @@ each of its rows, with
D\;\leftrightarrow\;[d_d, d(x)]
\end{align}
The algebra of hierarchical matrices under this continuous parameterization is
-review in \S\ref{sec:dict}. The complexity becomes
+reviewed in \S\ref{sec:dict}. With these substitutions, the complexity becomes
\begin{equation}
\begin{aligned}
\Sigma(E,\mu^*)