Error Control of the Vectorial Nondirective Stable Plane Wave Multilevel Fast Multipole Algorithm

Novel formulas are presented that allow the rapid estimation of the number of terms L that needs to be taken into account in the translation operator of the vectorial Nondirective Stable Plane Wave Multilevel Fast Multipole Algorithm (NSPWMLFMA). This is especially important for low frequencies, since the L needed for errorcontrollability can be substantially higher than the L required in the scalar case. Although these formulas were originally derived for use in the NSPWMLFMA, they are equally useful in at least three other fast matrix multiplication methods.