Comparison of the computational cost of a monte carlo and deterministic algorithm for computing bilinear forms of matrix powers

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

Citing 5
Cited 3

Monte Carlo algorithms: performance analysis for some computer architectures

Journal of Computational and Applied Mathematics
Matrix computations (3rd ed.)

Matrix computations (3rd ed.)
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms

The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
A new iterative Monte Carlo approach for inverse matrix problem

Journal of Computational and Applied Mathematics
Parallel resolvent Monte Carlo algorithms for linear algebra problems

Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods

Monte Carlo methods for matrix computations on the grid

Future Generation Computer Systems
Monte Carlo Numerical Treatment of Large Linear Algebra Problems

ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Advanced scalable algorithms for advanced architectures

CompSysTech '09 Proceedings of the International Conference on Computer Systems and Technologies and Workshop for PhD Students in Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.