Modern wireless cellular networks use massive multiple-input multiple-output (MIMO) technology. This technology involves operations with an antenna array at a base station that simultaneously serves multiple mobile devices which also use multiple antennas on their side. For this, various precoding and detection techniques are used, allowing each user to receive the signal intended for him from the base station. There is an important class of linear precoding called Regularized Zero-Forcing (RZF). In this work, we propose Adaptive RZF (ARZF) with a special kind of regularization matrix with different coefficients for each layer of multi-antenna users. These regularization coefficients are defined by explicit formulas based on Singular Value Decomposition (SVD) of user channel matrices. We study the optimization problem, which is solved by the proposed algorithm, with the connection to other possible problem statements. We prove theoretical estimates of the number of conditionality of the inverse covariance matrix of the ARZF method and the standard RZF method, which is important for systems with fixed computational accuracy. Finally, We compare the proposed algorithm with state-of-the-art linear precoding algorithms on simulations with the Quadriga channel model. The proposed approach provides a significant increase in quality with the same computation time as in the reference methods.