From: couturie <couturie@extinction>
Date: Mon, 2 Nov 2015 18:53:40 +0000 (-0500)
Subject: Merge branch 'master' of ssh://info.iut-bm.univ-fcomte.fr/kahina_paper1
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper1.git/commitdiff_plain/493d5e9fdd4a38a9b7fabdc3fbb9e4835ad6efea?ds=sidebyside;hp=-c

Merge branch 'master' of ssh://info.iut-bm.univ-fcomte.fr/kahina_paper1
---

493d5e9fdd4a38a9b7fabdc3fbb9e4835ad6efea
diff --combined paper.tex
index 20686d2,c78df7b..e4873d7
--- a/paper.tex
+++ b/paper.tex
@@@ -312,8 -312,7 +312,7 @@@ The convergence condition determines th
  
  \begin{equation}
  \label{eq:Aberth-Conv-Cond}
- \forall i \in
- [1,n];\frac{z_{i}^{k}-z_{i}^{k-1}}{z_{i}^{k}}<\xi
+ \forall i \in [1,n];\vert\frac{z_{i}^{k}-z_{i}^{k-1}}{z_{i}^{k}}\vert<\xi
  \end{equation}
  
  
@@@ -394,7 -393,7 +393,7 @@@ There are many schemes for the simultan
  polynomial. Several works on different methods and issues of root
  finding have been reported in~\cite{Azad07, Gemignani07, Kalantari08, Skachek08, Zhancall08, Zhuall08}. However, Durand-Kerner and Ehrlich-Aberth methods are the most practical choices among
  them~\cite{Bini04}. These two methods have been extensively
 -studied for parallelization due to their intrinsics, i.e. the
 +studied for parallelization due to their intrinsics parallelism, i.e. the
  computations involved in both methods has some inherent
  parallelism that can be suitably exploited by SIMD machines.
  Moreover, they have fast rate of convergence (quadratic for the
@@@ -413,11 -412,8 +412,11 @@@ Optoelectronic Transpose Interconnectio
  algorithms are mapped on an OTIS-2D torus using N processors. This
  solution needs N processors to compute N roots, which is not
  practical for solving polynomials with large degrees.
 -Until very recently, the literature doen not mention implementations able to compute the roots of
 -large degree polynomials (higher then 1000) and within small or at least tractable times. Finding polynomial roots rapidly and accurately is the main objective of our work. 
 +%Until very recently, the literature did not mention implementations
 +%able to compute the roots of large degree polynomials (higher then
 +%1000) and within small or at least tractable times.
 +
 +Finding polynomial roots rapidly and accurately is the main objective of our work. 
  With the advent of CUDA (Compute Unified Device
  Architecture), finding the roots of polynomials receives a new attention because of the new possibilities to solve higher degree polynomials in less time. 
  In~\cite{Kahinall14} we already proposed the first implementation