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b/figures/log_exp.plot index a1ba5d8..edd5ab1 100644 --- a/figures/log_exp.plot +++ b/figures/log_exp.plot @@ -14,5 +14,5 @@ set style line 1 lc rgb '#0060ad' lt 1 lw 2 pt 1 ps 1.5 # --- blue set style line 2 lc rgb '#dd181f' lt 1 lw 2 pt 5 ps 1.5 # --- red plot'log_exp.txt' index 0 using 1:4 t "No log exp" with linespoints ls 2,\ - 'log_exp.txt' index 0 using 1:2 t "with log exp" with linespoints ls 1,\ - 'log_exp.txt'index 1 using 1:2 t "with_log_exp" with linespoints ls 1 + 'log_exp.txt' index 0 using 1:2 t "with log exp" with linespoints ls 1,\ + 'log_exp.txt'index 1 using 1:2 t "with_log_exp" with linespoints ls 1 diff --git a/figures/log_exp.txt b/figures/log_exp.txt index 47874d7..afe212b 100644 --- a/figures/log_exp.txt +++ b/figures/log_exp.txt @@ -13,8 +13,9 @@ # Second index block (index 1) #EA With_log_exp -#Taille_Poly times nb iter -4500 0.946749 23 +#Taille_Poly times nb iter +4000 0.506183 23 +#4500 0.946749 23 5000 0.769945 33 6000 1.38447 48 10000 2.15026 32 diff 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exp" with linespoints ls 2,\ 'log_exp_Sparse.txt' index 0 using 1:2 t "with log exp" with linespoints ls 1,\ - 'log_exp_Sparse.txt'index 1 using 1:2 t "with_log_exp" with linespoints ls 1 \ No newline at end of file + 'log_exp_Sparse.txt' index 1 using 1:2 t "with_log_exp" with linespoints ls 1 \ No newline at end of file diff --git a/figures/log_exp_Sparse.txt b/figures/log_exp_Sparse.txt index aa2cff5..0dc90fc 100644 --- a/figures/log_exp_Sparse.txt +++ b/figures/log_exp_Sparse.txt @@ -14,7 +14,8 @@ 150000 18.6746 11 16.3098 16 # Second index block (index 1) -#Taille_Poly times nb iter +#Taille_Poly times nb iter +150000 18.6746 11 200000 67.6199 22 300000 132.27 20 350000 159.65 18 diff --git a/paper.tex b/paper.tex index 4ce9747..c12aeda 100644 --- a/paper.tex +++ b/paper.tex @@ -672,6 +672,12 @@ The figure 3, show a comparison between the execution time of the Ehrlich-Aberth in fact, when the modulus of the roots are up than \textit{R} given in ~\ref{R},this exceed the limited number in the mantissa of floating points representations and can not compute the iterative function given in ~\ref{eq:Aberth-H-GS} to obtain the root solution, who justify the divergence of the classical Ehrlich-Aberth algorithm. However, applying log.exp solution given in ~\ref{sec2} took into account the limit of floating using the iterative function in(Eq.~\ref{Log_H1},Eq.~\ref{Log_H2}and allows to solve a very large polynomials degrees . +\begin{figure}[H] +\centering + \includegraphics[width=0.8\textwidth]{figures/log_exp_Sparse} +\caption{The impact of exp-log solution to compute very high degrees of polynomial.} +\label{fig:01} +\end{figure} %we report the performances of the exp.log for the Ehrlich-Aberth algorithm for solving very high degree of polynomial. -- 2.39.5