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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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 439, 2015, pp. 112–127.
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Il’in, V.P. Problems of Parallel Solution of Large Systems of Linear Algebraic Equations. J Math Sci 216, 795–804 (2016). https://doi.org/10.1007/s10958-016-2945-4
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DOI: https://doi.org/10.1007/s10958-016-2945-4