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

Authors:
Ivan Dimov;Vassil Alexandrov;Simon Branford;Christian Weihrauch
Affiliations:
Centre for Advanced Computing and Emerging Technologies, School of Systems Engineering, The University of Reading, Reading, UK;Centre for Advanced Computing and Emerging Technologies, School of Systems Engineering, The University of Reading, Reading, UK;Centre for Advanced Computing and Emerging Technologies, School of Systems Engineering, The University of Reading, Reading, UK;Centre for Advanced Computing and Emerging Technologies, School of Systems Engineering, The University of Reading, Reading, UK
Venue:
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part III
Year:
2006

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Abstract

In this paper we present error analysis for a Monte Carlo algorithm for evaluating bilinear forms of matrix powers. An almost Optimal Monte Carlo (MAO) algorithm for solving this problem is formulated. Results for the structure of the probability error are presented and the construction of robust and interpolation Monte Carlo algorithms are discussed. Results are presented comparing the performance of the Monte Carlo algorithm with that of a corresponding deterministic algorithm. The two algorithms are tested on a well balanced matrix and then the effects of perturbing this matrix, by small and large amounts, is studied.