diff --git a/EuroPar/2-amg-prec.tex b/EuroPar/2-amg-prec.tex
index 72de917..5e02fd1 100644
--- a/EuroPar/2-amg-prec.tex
+++ b/EuroPar/2-amg-prec.tex
@@ -1,4 +1,3 @@
-
 \section{Algebraic MultiGrid (AMG) Preconditioners}~\label{AMG}
 %
 MultiGrid methods are widely used as preconditioners of iterative
@@ -28,7 +27,7 @@ \section{Algebraic MultiGrid (AMG) Preconditioners}~\label{AMG}
 Jacobi or Gauss-Seidel, to reduce highly oscillatory error components,
 while the coarse-grid correction corresponds to the solution of the
 resulting residual equation in an appropriately chosen coarse space
-aimed at reducing the leftover error components. In the classical
+aimed at reducing the leftover error components. In the original
 multigrid approach, the coarser grid and the interpolation operator
 for transfer the coarse-grid solution to the original (fine) grid are
 predefined by the geometry of the problem. The recursive application
@@ -39,13 +38,13 @@ \section{Algebraic MultiGrid (AMG) Preconditioners}~\label{AMG}
 problem and relying only on system matrix entries. In this work we
 refer to an algebraic coarsening process based on aggregation of
 unknowns, where coarse-grid unknowns are agglomerates of the original
-unknowns. In particular, AMG preconditioners available in MLD2P4 rely
+ones. In particular, AMG preconditioners available in MLD2P4 rely
 on a decoupled version of \emph{the smoothed aggregation} algorithm
 described in~\cite{BrezinaVanek96,BrezinaVanek99}. This procedure is
 currently implemented on the host CPUs, therefore, for sake of space,
 we refer the reader to~\cite{mld2p4-2-guide} for more details on the
 algorithm and its parallel implementation. 
-Our main aim here is to describe all the main Linear Algebra
+Our main aim here is to describe all the basic linear algebra
 operations needed for the application of the AMG preconditioner within
 an iterative  linear solver, since their efficient implementation on
 GPUs was the main focus of this work. 
@@ -87,7 +86,7 @@ \section{Algebraic MultiGrid (AMG) Preconditioners}~\label{AMG}
 level $k$ for relaxation. 
 Main computational kernels in the application of the preconditioner
 are then sparse matrix-vector multiplications and inversion of the
-matrix operator $M^k$. In the simple case of Jacobi method,
+matrix operator $M^k$. In the simple case of Jacobi method is
 $M^k=diag(A^k)$, therefore it corresponds to a highly parallel vector
 update operation. On the other hand, more robust iterative methods,
 such as the Gauss-Seidel method or incomplete factorizations, are