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Comparison of the computational cost of a Monte Carlo and deterministic algorithm for computing bilinear forms of matrix powers

Weihrauch, C., Dimov, I., Branford, S. and Alexandrov, V. (2006) Comparison of the computational cost of a Monte Carlo and deterministic algorithm for computing bilinear forms of matrix powers. Lecture Notes in Computer Science, 3993. pp. 640-647. ISSN 0302-9743 3-540-34383-0

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Abstract/Summary

In this paper we consider bilinear forms of matrix polynomials and show that these polynomials can be used to construct solutions for the problems of solving systems of linear algebraic equations, matrix inversion and finding extremal eigenvalues. An almost Optimal Monte Carlo (MAO) algorithm for computing bilinear forms of matrix polynomials is presented. Results for the computational costs of a balanced algorithm for computing the bilinear form of a matrix power is presented, i.e., an algorithm for which probability and systematic errors are of the same order, and this is compared with the computational cost for a corresponding deterministic method.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Systems Engineering
ID Code:15452
Uncontrolled Keywords:Monte Carlo algorithms, matrix computations, performance analysis, computational cost, iterative process
Additional Information:Proceedings Paper 6th International Conference on Computational Science (ICCS 2006) MAY 28-31, 2006 Reading, ENGLAND

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