where for $k\in\{1,\ldots,s\}$, $x^k=[X_1^k,\ldots,X_L^k]$ is a solution of the global linear
system.
%The advantage such a method is that the Krylov subspace does not need to be spanned by an orthogonal basis.
-The advantage of such a method is that the Krylov subspace need neither to be spanned by an orthogonal
-basis nor synchronizations between the different clusters to generate this basis.
+The advantage of such a Krylov subspace is that we need neither an orthogonal basis nor synchronizations
+between the different clusters to generate this basis.
