Jaroslaw Bylina

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In this paper a distributed iterative GMRES algorithm for solving huge and sparse linear systems (that appear in the Markov chain analysis of queueing network models) is considered. It is implemented using the MPI standard on a collection of Linux machines and the emphasis is put upon the size of linear systems being solved and possibility of storing huge(More)
The authors consider the use of the parallel iterative methods for solving large sparse linear equation systems resulting from Markov chains-on a computer cluster. A combination of Jacobi and Gauss-Seidel iterative methods is examined in a parallel version. Some results of experiments for sparse systems with over 3 times 10<sup>7</sup> equations and about 2(More)
We investigate condition numbers of matrices that appear during solving systems of linear equations. We consider iterative methods to solve the equations, namely Jacobi and Gauss-Seidel methods. We examine the influence of the condition number on convergence of these iterative methods. We study numerical aspects of relations between the condition number and(More)
The paper contains the review and the discussion on modelling communication networks with the use of queuing models and Markov chains. It shows how to take into account various characteristics of real systems – like some control mechanisms and the traffic self-similarity. There are presented two mechanisms modelled with Markov chains: the RED algorithm in(More)
In this article we evaluate some strategies of parallelizing nested loops on Intel Xeon Phi on the example of the WZ factorization for dense matrices. We employ both parallelism and vectorization to accelerate nested loops on manycore coprocessor. For random dense square matrices with the dominant diagonal we report the execution time and the performance of(More)