Abstract
The paper considers some modern problems arising in developing parallel algorithms for solving large systems of linear algebraic equations with sparse matrices occurring in mathematical modeling of real-life processes and phenomena on a multiprocessor computer system (MCS). Two main requirements to methods and technologies under consideration are fast convergence of iterations and scalable parallelism, which are intrinsically contradictory and need a special investigation. The paper analyzes main trends is developing preconditioned iterative methods in Krylov’s subspaces based on algebraic domain decomposition and principles of their program implementation on a heterogeneous MCS with hierarchical memory structure.
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