X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/book_gpu.git/blobdiff_plain/4932967a1c684dc3f7ed04c19144101278b79972..65f8be28e79668334c6fcbc3a2af46a7c8a2eab0:/BookGPU/Chapters/chapter16/ef.tex

diff --git a/BookGPU/Chapters/chapter16/ef.tex b/BookGPU/Chapters/chapter16/ef.tex
index b0967a9..812c97a 100644
--- a/BookGPU/Chapters/chapter16/ef.tex
+++ b/BookGPU/Chapters/chapter16/ef.tex
@@ -52,7 +52,7 @@ significant savings in simulation time.
 % One simple way to estimate $x((m+k)T)$ is to use the information at
 % $mT$ and $(m-1)T$, which leads to the forward-Euler method as
 To estimate $x((m+k)T)$,
-a forward-Euler\index{forward-Euler} style jumping relies only on $x(mT)$ and $x((m-1)T)$,
+a forward Euler\index{Euler!forward Euler} style jumping relies only on $x(mT)$ and $x((m-1)T)$,
 i.e.,
 \[
    x((m+k)T)
@@ -61,14 +61,14 @@ i.e.,
 \]
 However, this approach is inefficient due to its restriction on
 envelope step $k$, since larger $k$ usually causes instability.
-Instead, backward-Euler\index{backward-Euler} jumping,
+Instead, backward Euler\index{Euler!backward Euler} jumping,
 %and the equation becomes
 \[
   x((m+k)T)-x(mT) = k\left[x((m+k)T)-x((m+k-1)T)\right],
 \]
 allows larger envelope steps.
 Here $x((m+k-1)T)$ is the unknown variable to be solved
-by Newton iteration\index{Newton iteration},
+by Newton iteration\index{iterative method!Newton iteration},
 and $x((m+k)T)$ is dependent on $x((m+k-1)T)$
 in each iteration.
 % Forward-Euler may be used to generate the initial guess.
@@ -107,7 +107,7 @@ Different integration rules can be applied to
 the computation of sensitivity matrix.
 It can be easily derived that,
 %for one signal period with $M$ time steps,
-if the DAE is integrated with backward-Euler rule,
+if the DAE is integrated with backward Euler rule,
 the sensitivity is
 \[
    J = \frac{\ud x_M}{\ud x_0}
@@ -133,7 +133,7 @@ In summary, the envelope-following method is fundamentally
 a boosted version of traditional transient analysis,
 with certain skips over several periods and a Newton iteration
 to update or correct the errors brought by the skips,
-as is exhibited by Fig.~\ref{fig:ef_flow}.
+as is exhibited by Figure~\ref{fig:ef_flow}.
 \begin{figure}[!tb]
 \centering
 \resizebox{.7\textwidth}{!}{\input{./Chapters/chapter16/figures/ef_flow.pdf_t}}