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M2X, X2X, X2L in three-dimensional Laplace's equation

In this appendix we describe the derivation of M2X, X2X and X2L translation formulae in three-dimensional Laplace's equation and estimate the computational costs for these translations. Notice that Greengard and Rokhlin [36] estimate the cost under the following conditions:

\begin{eqnarray*}S\mbox{exp} = \sum_{k=1}^s M(k) \approx p^2 ,\quad s \approx p
\end{eqnarray*}




 

Ken-ichi Yoshida
2001-07-28