Problems of Parallel Solution of Large Systems of Linear Algebraic Equations

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...

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Bibliographic Details
Published in:	Journal of mathematical sciences (New York, N.Y.) Vol. 216; no. 6; pp. 795 - 804
Main Author:	Il’in, V. P.
Format:	Journal Article
Language:	English
Published:	New York Springer US 02.08.2016 Springer
Subjects:	Algorithms Mathematics Mathematics and Statistics Multiprocessing
ISSN:	1072-3374, 1573-8795
Online Access:	Get full text
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Summary:	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.
ISSN:	1072-3374 1573-8795
DOI:	10.1007/s10958-016-2945-4