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The multilevel matrix decomposition algorithm (MLMDA) was originally developed by Michielsen and Boag for 2D TMz scattering problems and later implemented in 3D by Rius et al. The 3D MLMDA was particularly efficient and accurate for piece-wise planar objects such as printed antennas. However, for arbitrary 3D problems it was not as efficient as the multilevel fast multipole algorithm (MLFMA) and the matrix compression error was too large for practical applications. This paper will introduce some improvements in 3D MLMDA, like new placement of equivalent functions and SVD postcompression. The first is crucial to have a matrix compression error that converges to zero as the compressed matrix size increases. As a result, the new MDA-SVD algorithm is comparable with the MLFMA and the adaptive cross approximation (ACA) in terms of computation time and memory requirements. Remarkably, in high-accuracy computations the MDA-SVD approach obtains a matrix compression error one order of magnitude smaller than ACA or MLFMA in less computation time. Like the ACA, the MDA-SVD algorithm can be implemented on top of an existing MoM code with most commonly used Green's functions, but the MDA-SVD is much more efficient in the analysis of planar or piece-wise planar objects, like printed antennas.