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In order to efficiently solve large dense complex linear systems arising from the electric field integral equations formulation of electromagnetic problems, matrix decomposition algorithm-singular value decomposition (MDA-SVD) is used to accelerate the matrix-vector product (MVP) operation. Based on the symmetry of the impedance matrix, a modified multilevel simple sparse method (M-MLSSM) is proposed. Combining MDA and M-MLSSM, the authors obtain a sparse representation of the impedance matrix and construct a fast MVP operation. A perfectly electrically conducting sphere and the series-fed microstrip antenna array are simulated to demonstrate the validity of the proposed method. Moreover, numerical experiments demonstrate that combined MDA and M-MLSSM can accelerate the MVP operation and reduce memory requirements by at least half an order of magnitude compared to MDA-SVD.