Relu tout à part la section Expermiental study

[kahina_paper1.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 104bcbe3f09960c129674f962433e64c584e739c..c68c068e778142319de104099edcc1030fe3b3f5 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -232,6 +232,7 @@ The initialization of a polynomial p(z) is done by setting each of the $n$ compl
 :
 
 \begin{equation}
 :
 
 \begin{equation}

+\label{eq:SimplePolynome}

   p(z)=\sum{a_{i}z^{n-i}} , a_{n} \neq 0,a_{0}=1, a_{i}\subset C
 \end{equation}
 
   p(z)=\sum{a_{i}z^{n-i}} , a_{n} \neq 0,a_{0}=1, a_{i}\subset C
 \end{equation}
 


@@ -248,6 +249,7 @@ performed this choice by selecting complex numbers along different
 circles and relies on the result of~\cite{Ostrowski41}.
 
 \begin{equation}
 circles and relies on the result of~\cite{Ostrowski41}.
 
 \begin{equation}

+\label{eq:radiusR}

 %%\begin{align}
 \sigma_{0}=\frac{u+v}{2};u=\frac{\sum_{i=1}^{n}u_{i}}{n.max_{i=1}^{n}u_{i}};
 v=\frac{\sum_{i=0}^{n-1}v_{i}}{n.min_{i=0}^{n-1}v_{i}};\\
 %%\begin{align}
 \sigma_{0}=\frac{u+v}{2};u=\frac{\sum_{i=1}^{n}u_{i}}{n.max_{i=1}^{n}u_{i}};
 v=\frac{\sum_{i=0}^{n-1}v_{i}}{n.min_{i=0}^{n-1}v_{i}};\\


@@ -568,14 +570,14 @@ $kernel\_update\_Log(d\_z^{k})$\;
 }
 \end{algorithm}
 
 }
 \end{algorithm}
 

-The first form executes the formula (8) if the modulus is of the current complex is less than the radius i.e. ($ |z^{k}_{i}|<= R$), else the kernel executes formulas (13,14). The radius R is evaluated as :
+The first form executes formula \ref{eq:SimplePolynome} if the modulus of the current complex is less than the a certain value called the radius i.e. ($ |z^{k}_{i}|<= R$), else the kernel executes formulas (Eq.~\ref{deflncomplex},Eq.~\ref{defexpcomplex}). The radius $R$ is evaluated as :

 
 $$R = \exp( \log(DBL\_MAX) / (2*n) )$$ where $DBL\_MAX$ stands for the maximum representable double value.
 
 The last kernel verifies the convergence of the roots after each update of $Z^{(k)}$, according to formula. We used the functions of the CUBLAS Library (CUDA Basic Linear Algebra Subroutines) to implement this kernel. 
 
 
 $$R = \exp( \log(DBL\_MAX) / (2*n) )$$ where $DBL\_MAX$ stands for the maximum representable double value.
 
 The last kernel verifies the convergence of the roots after each update of $Z^{(k)}$, according to formula. We used the functions of the CUBLAS Library (CUDA Basic Linear Algebra Subroutines) to implement this kernel. 
 

-The kernels terminates it computations when all the root are converged. Finally, the solution of the  root finding problem is copied back from the GPU global memory to the CPU memory. We use the communication functions of CUDA for the memory allocations in the GPU \verb=(cudaMalloc())= and the data transfers from the CPU memory to the GPU memory \verb=(cudaMemcpyHostToDevice)=
-or from the GPU memory to the CPU memory \verb=(cudaMemcpyDeviceToHost))=. 
+The kernels terminate it computations when all the roots converge. Finally, the solution of the root finding problem is copied back from GPU global memory to CPU memory. We use the communication functions of CUDA for the memory allocation in the GPU \verb=(cudaMalloc())= and for data transfers from the CPU memory to the GPU memory \verb=(cudaMemcpyHostToDevice)=
+or from GPU memory to CPU memory \verb=(cudaMemcpyDeviceToHost))=. 

 %%HIER END MY REVISIONS (SIDER)
 \subsection{Experimental study}
 
 %%HIER END MY REVISIONS (SIDER)
 \subsection{Experimental study}