Abstract
In this paper we deal with performance analysis of Monte Carlo algorithm for large linear algebra problems. We consider applicability and efficiency of the Markov chain Monte Carlo for large problems, i.e., problems involving matrices with a number of non-zero elements ranging between one million and one billion. We are concentrating on analysis of the almost Optimal Monte Carlo (MAO) algorithm for evaluating bilinear forms of matrix powers since they form the so-called Krylov subspaces.
Results are presented comparing the performance of the Robust and Non-robust Monte Carlo algorithms. The algorithms are tested on large dense matrices as well as on large unstructured sparse matrices.
Partially supported by the Bulgarian Ministry of Education and Science, under grant I-1405/2004. The authors would like to acknowledge the support of the European Commission’s Research Infrastructures activity of the Structuring the European Research Area programme, contract number RII3-CT-2003-506079 (HPC-Europa).
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Dimov, I., Alexandrov, V., Papancheva, R., Weihrauch, C. (2007). Monte Carlo Numerical Treatment of Large Linear Algebra Problems. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds) Computational Science – ICCS 2007. ICCS 2007. Lecture Notes in Computer Science, vol 4487. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72584-8_99
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DOI: https://doi.org/10.1007/978-3-540-72584-8_99
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