Monte Carlo numerical treatment of large linear algebra problems
Dimov, I., Alexandrov, V., Papancheva, R. and Weihrauch, C. (2007) Monte Carlo numerical treatment of large linear algebra problems. Lecture Notes in Computer Science, 4487. pp. 747-754. ISSN 0302-9743 9783540725831
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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.