Abstract
Approximate inverse matrix semi-direct methods for solving numerically linear systems on parallel processors are presented. The derived first and second order iterative methods possessing a high level of parallelism are based on the multiple explicit Jacobi iteration and originated by the approximation of the economized Chebychev polynomial and Neumann series to the inverse matrix. The convergence analysis of the proposed stationary and non-stationary explicit iterative schemes is developed and numerical results for a model problem are given.
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