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An innovative approach is presented for analyzing finite arrays of regularly spaced elements. We review the recently proposed Array Decomposition Method, which exploits the block-Toeplitz property of regularly spaced arrays for significant storage reduction. To further reduce storage, in this paper we incorporate a multipole expansion to treat distant element interactions. The suggested approach overcomes the matrix storage bottleneck associated with integral equation methods, resulting in fixed and minimal matrix storage for any sized array (on the same order as the storage of a single array element). Hence, fast and rigorous analysis of very large finite arrays can be accomplished with limited resources.