Implicit iterative scheme based on the pseudo-inversion algorithm and its application

A new version of the implicit iterative scheme is proposed for the implementation of which only matrix-vector computational procedures are required. This makes the proposed computational scheme potentially highly efficient for solving a wide class of high-dimensional problems on modern high-performance computing platforms, such as Nvidia Cuda. It is shown that the proposed algorithms can be used to solve ill-conditioned linear systems and least squares problems, as well as to construct iterative regularization algorithms. The results of computational experiments are presented, confirming the effectiveness of the proposed computational algorithms.