From: couturie Date: Mon, 2 Nov 2015 13:45:37 +0000 (-0500) Subject: correct X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper1.git/commitdiff_plain/84bdc1ad86104770f6df03822fbbd4284fa7a7b1?hp=--cc correct --- 84bdc1ad86104770f6df03822fbbd4284fa7a7b1 diff --git a/paper.tex b/paper.tex index 4e2180e..b3e3076 100644 --- a/paper.tex +++ b/paper.tex @@ -183,7 +183,7 @@ drastically increases like the degrees of high polynomials. It is expected that parallelization of these algorithms will improve the convergence time. -Many authors have dealt with the parallelisation of +Many authors have dealt with the parallelization of simultaneous methods, i.e. that find all the zeros simultaneously. Freeman~\cite{Freeman89} implemeted and compared DK, EA and another method of the fourth order proposed by Farmer and Loizou~\cite{Loizon83}, on a 8- processor linear @@ -194,7 +194,7 @@ Freeman and Bane~\cite{Freemanall90} considered asynchronous algorithms, in which each processor continues to update its approximations even though the latest values of other $z_i((k))$ have not been received from the other processors, in contrast with synchronous algorithms where it would wait those values before making a new iteration. -Couturier and al~\cite{Raphaelall01} proposed two methods of parallelisation for +Couturier and al~\cite{Raphaelall01} proposed two methods of parallelization for a shared memory architecture and for distributed memory one. They were able to compute the roots of polynomials of degree 10000 in 430 seconds with only 8 personal computers and 2 communications per iteration. Comparing to the sequential implementation @@ -365,7 +365,7 @@ R = exp(log(DBL_MAX)/(2*n) ); \label{secStateofArt} The main problem of simultaneous methods is that the necessary time needed for convergence is increased when we increase -the degree of the polynomial. The parallelisation of these +the degree of the polynomial. The parallelization of these algorithms is expected to improve the convergence time. Authors usually adopt one of the two following approaches to parallelize root finding algorithms. The first approach aims at reducing the total number of