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In order to efficiently and accurately analyze the scattering of multilayer microstrip structures, the matrix decomposition algorithm - singular value decomposition (MDA-SVD) is used to accelerate the matrix-vector multiplication operations. MDA-SVD is purely algebraic; hence, its formulation and implementation are integral equation kernel independent. It utilizes the SVD algorithm to reduce the memory requirement and solution time of the matrix decomposition algorithm. The numerical results demonstrate the efficiency of the proposed method.