The following are some comparisons between the FMM and WCM:

(1) A large part of the CPU time of the FMM is spent on the iteration. However, in WCM, iteration is much fast since the matrix is computed and saved in memory.

(2) In FMM, the M2L transforms must be optimaized since it is re-computed in each iteration. In wavelet method, M2L is used only once (in matrix computation).

Thus we conclude that the WCM is more suitable for problem needing relatively large number of iterations to converge, while the FMM is efficient when the number of iterations is small, e.g., less than 50.