Current iterative multiple-input multiple-output (MIMO) detectors suffer from slow convergence when the wireless channel is ill-conditioned. The ill-conditioning is mainly caused by spatial correlation between channel columns corresponding to the same user equipment, known as intra-user interference. In addition, in the emerging MIMO systems using an extremely large aperture array (ELAA), spatial non-stationarity can make the channel even more ill-conditioned. In this paper, user-wise singular value decomposition (UW-SVD) is proposed to accelerate the convergence of iterative MIMO detectors. Its basic principle is to perform SVD on each user's sub-channel matrix to eliminate intra-user interference. Then, the MIMO signal model is effectively transformed into an equivalent signal (e-signal) model, comprising an e-channel matrix and an e-signal vector. Existing iterative algorithms can be used to recover the e-signal vector, which undergoes post-processing to obtain the signal vector. It is proven that the e-channel matrix is better conditioned than the original MIMO channel for spatially correlated (ELAA-)MIMO channels. This implies that UW-SVD can accelerate current iterative algorithms, which is confirmed by our simulation results. Specifically, it can speed up convergence by up to 10 times in both uncoded and coded systems.