1 files changed, 10 insertions, 6 deletions
diff --git a/eigen/doc/TutorialSparse.dox b/eigen/doc/TutorialSparse.dox
index ee206cc..3529074 100644
--- a/eigen/doc/TutorialSparse.dox
+++ b/eigen/doc/TutorialSparse.dox
@@ -83,7 +83,7 @@ There is no notion of compressed/uncompressed mode for a SparseVector.
 
 \section TutorialSparseExample First example
 
-Before describing each individual class, let's start with the following typical example: solving the Laplace equation \f$ \nabla u = 0 \f$ on a regular 2D grid using a finite difference scheme and Dirichlet boundary conditions.
+Before describing each individual class, let's start with the following typical example: solving the Laplace equation \f$ \Delta u = 0 \f$ on a regular 2D grid using a finite difference scheme and Dirichlet boundary conditions.
 Such problem can be mathematically expressed as a linear problem of the form \f$ Ax=b \f$ where \f$ x \f$ is the vector of \c m unknowns (in our case, the values of the pixels), \f$ b \f$ is the right hand side vector resulting from the boundary conditions, and \f$ A \f$ is an \f$ m \times m \f$ matrix containing only a few non-zero elements resulting from the discretization of the Laplacian operator.
 
 <table class="manual">
@@ -253,15 +253,19 @@ SparseMatrix<double> A, B;
 B = SparseMatrix<double>(A.transpose()) + A;
 \endcode
 
-Some binary coefficient-wise operators can also mix sparse and dense expressions:
+Binary coefficient wise operators can also mix sparse and dense expressions:
 \code
 sm2 = sm1.cwiseProduct(dm1);
-dm1 += sm1;
+dm2 = sm1 + dm1;
+dm2 = dm1 - sm1;
 \endcode
+Performance-wise, the adding/subtracting sparse and dense matrices is better performed in two steps. For instance, instead of doing <tt>dm2 = sm1 + dm1</tt>, better write:
+\code
+dm2 = dm1;
+dm2 += sm1;
+\endcode
+This version has the advantage to fully exploit the higher performance of dense storage (no indirection, SIMD, etc.), and to pay the cost of slow sparse evaluation on the few non-zeros of the sparse matrix only.
 
-However, it is not yet possible to add a sparse and a dense matrix as in <tt>dm2 = sm1 + dm1</tt>.
-Please write this as the equivalent <tt>dm2 = dm1; dm2 += sm1</tt> (we plan to lift this restriction
-in the next release of %Eigen).
 
 %Sparse expressions also support transposition:
 \code