**Steps 1-2.**Same as the steps 1-2 in the algorithm described in chapter 2.**Step 3.**Computation of the multipole moments:In this step we use (3.147) and (3.148) for the computation of the multipole moments associated with leaves. Also, we use (3.149) and (3.150) for M2M translations tracing the tree structure of cells upward (decreasing ).

**Step 4.**Computation of the local expansion: In this step we use (3.152) and (3.153) for M2L translations and (3.154) and (3.155) for L2L translations tracing the tree structure of cells downward (increasing ).**Step 5.**Evaluation of the integral in (3.118): In this step we use (3.119) for the direct computation and use (3.130) for the evaluation of contributions from the local expansion.