The computational bottleneck in this code comes from converting an existing dense matrix into a sparse matrix. If the matrix has only a few non-zero entries, sparse matrix multiplication will indeed be much more efficient. However, there may be a large overhead cost in constructing the sparse matrix from the dense matrix that exists. The cost of the conversion process may therefore negate the savings gained in the multiplication.The best option is to construct the matrix A to be sparse from the beginning, rather than building it as a dense matrix and converting it:
>> A = sparse(i, j, s, m, n);
This will provide the performance gain of the sparse multiplication without the overhead cost of converting a dense matrix into a sparse matrix. However, if it s not possible to do so, then it could prove more efficient to simply perform a dense matrix multiplication.
