iteration and $MinTcm$ is the communication time of the slowest processor from
the first iteration. The model computes the maximum computation time
with scaling factor from each node added to the communication time of the \subsection{The verifications of the proposed method}
-\label{sec.verif}
+\label{sec.verif.method}
The precision of the proposed algorithm mainly depends on the execution time prediction model defined in
EQ(\ref{eq:perf}) and the energy model computed by EQ(\ref{eq:energy}).
The energy model is also significantly dependent on the execution time model because the static energy is
equal to the execution time of one iteration as in EQ(\ref{eq:perf}) multiplied
by the number of iterations of that application.
-This prediction model is developed from our model for predicting the execution time of
+This prediction model is developed from the model for predicting the execution time of
message passing distributed applications for homogeneous architectures~\cite{Our_first_paper}.
-The execution time prediction model is used in our method for optimizing both
+The execution time prediction model is used in the method for optimizing both
energy consumption and performance of iterative methods, which is presented in the
following sections.
between the energy curve EQ~(\ref{eq:enorm}) and the performance
curve EQ~(\ref{eq:pnorm_inv}) over all available sets of scaling factors. This
represents the minimum energy consumption with minimum execution time (maximum
-performance) at the same time, see figure~(\ref{fig:r1}) or figure~(\ref{fig:r2}). Then our objective
+performance) at the same time, see figure~(\ref{fig:r1}) or figure~(\ref{fig:r2}). Then the objective
function has the following form:
\begin{equation}
\label{eq:max}
passing iterative synchronous applications, fast nodes have to wait for the slower ones to finish their
computations before being able to synchronously communicate with them as in figure (\ref{fig:heter}).
These periods are called idle or slack times.
-Our algorithm takes into account this problem and tries to reduce these slack times when selecting the
+The algorithm takes into account this problem and tries to reduce these slack times when selecting the
frequency scaling factors vector. At first, it selects initial frequency scaling factors that increase
the execution times of fast nodes and minimize the differences between the computation times of
fast and slow nodes. The value of the initial frequency scaling factor for each node is inversely
\end{algorithm}
\subsection{The verifications of the proposed algorithm}
-\label{sec.verif}
+\label{sec.verif.algo}
The precision of the proposed algorithm mainly depends on the execution time prediction model defined in
EQ(\ref{eq:perf}) and the energy model computed by EQ(\ref{eq:energy}).
The energy model is also significantly dependent on the execution time model because the static energy is
