Despite the extensive use of a centralized approach to design receivers at the base station for massive multiple-input multiple-output (M-MIMO) systems, their actual implementation is a major challenge due to several bottlenecks imposed by the large number of antennas. One way to deal with this problem is by fully decentralizing the classic zero-forcing receiver across multiple processing nodes based on the gradient descent method. In this paper, we first explicitly relate this decentralized receiver to a distributed version of the Kaczmarz algorithm and to the use of the successive interference cancellation (SIC) philosophy to mitigate the residual across nodes. In addition, we propose two methods to further accelerate the initial convergence of these iterative decentralized receivers by exploring the connection with the Kaczmarz algorithm: 1) a new Bayesian distributed receiver, which can eliminate noise on an iteration basis; 2) a more practical method for choosing the relaxation parameter. The discussion also consider spatial non-stationarities that arise when the antenna arrays are extremely large (XL-MIMO). We were able to improve the numerical results for both spatially stationary and non-stationary channels, but mainly the non-stationary performance can still be improved compared to the centralized ZF receiver. Future research directions are provided with the aim of further improving the applicability of the receiver based on the principle of successive residual cancellation (SRC).