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
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
\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
