The scattering solution from N scatterers, each of whose scattered field is approximated by M harmonics is an NM unknown problem. A straightforward solution to this problem can be obtained by casting it into an NM linear algebraic equation. The solution of the linear algebraic equation will involve order N3M3 flouting point operations. However, via the use of a recursive algorithm and the translation formula, an order N2M3 algorithm to solve such a problem is possible.
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Weng Cho Chew (1989) studied this question.
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