Implicit iterative schemes based on singular decomposition and regularizing algorithms

A new version of the simple iterations implicit method based on the singular value decomposition is proposed. It is shown that this variant of the simple iterations implicit method can significantly improve the computational stability of the algorithm and at the same time provides a high rate of its convergence. The application of the simple iterations implicit method based on the singular value decomposition for the development of iterative regularization algorithms is considered. The proposed algorithms can be effectively used to solve a wide class of ill-posed and ill-conditioned computational problems.