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Chernov

Solving systems of linear algebraic equations by preconditioning on graphics processing units
Engineering Education # 01, January 2013
DOI: 10.7463/0113.0525190
The authors consider an algorithm for solving systems of linear algebraic equations (SLAE) with preconditions. The authors introduce parallel algorithms and software for image processing devices that implement the basic operations of the algorithm - multiplication of the matrix by a set of vectors and solutions of a block triangular SLAE. The results of extensive studies of effectiveness of the proposed algorithmic and software solutions are provided in this paper. These results show a fairly high efficiency of the developed algorithms and software for multiplication of the matrix by a set of vectors. Acceleration of computations in this case is four to sixteen times. Algorithms and programs for solving the block triangular SLAE showed satisfactory results which allow to expect an acceptable acceleration for practically significant SLAE of high dimension and when using professional GPU.
 
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