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 article considers the effectiveness of various methods used to solve systems of linear equations (which emerge while modeling computer networks and systems with Markov chains) and the practical influence of the methods applied on accuracy. The paper considers some hybrids of both direct and iterative methods. Two varieties of the Gauss elimination will(More)