Monte Carlo Numerical Treatment of Large Linear Algebra Problems

Authors:
Ivan Dimov;Vassil Alexandrov;Rumyana Papancheva;Christian Weihrauch
Affiliations:
Centre for Advanced Computing and Emerging Technologies, School of Systems Engineering, The University of Reading, Whiteknights, PO Box 225, Reading, RG6 6AY, UK and Institute for Parallel Process ...;Centre for Advanced Computing and Emerging Technologies, School of Systems Engineering, The University of Reading, Whiteknights, PO Box 225, Reading, RG6 6AY, UK;Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev 25 A, 1113 Sofia, Bulgaria;Centre for Advanced Computing and Emerging Technologies, School of Systems Engineering, The University of Reading, Whiteknights, PO Box 225, Reading, RG6 6AY, UK
Venue:
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Year:
2007

Citing 2
Cited 2

Error analysis of a monte carlo algorithm for computing bilinear forms of matrix powers

ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part III
Comparison of the computational cost of a monte carlo and deterministic algorithm for computing bilinear forms of matrix powers

ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part III

Stochastic algorithms in linear algebra: beyond the Markov chains and von Neumann-Ulam scheme

NMA'10 Proceedings of the 7th international conference on Numerical methods and applications
Investigating scaling behaviour of monte carlo codes for dense matrix inversion

Proceedings of the second workshop on Scalable algorithms for large-scale systems

Quantified Score

Hi-index	0.00

Visualization

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.