A Monte Carlo Approach for Finding More than One Eigenpair

Authors:
Michael Mascagni;Aneta Karaivanova
Affiliations:
-;-
Venue:
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Year:
2002

Citing 3
Cited 1

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Random number generation and quasi-Monte Carlo methods
Monte Carlo Techniques for Estimating the Fiedler Vector in Graph Applications

ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Matrix Computations Using Quasirandom Sequences

NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications

Computing the principal eigenelements of some linear operators using a branching Monte Carlo method

Journal of Computational Physics

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Abstract

The Monte Carlo method has been successfully used for computing the extreme (largest and smallest in magnitude) eigenvalues of matrices. In this paper we study computing eigenvectors as well with the Monte Carlo approach. We propose and study a Monte Carlo method based on applying the ergodic theorem and compare the results with those produced by a Monte Carlo version of the power method. We also study the problem of computing more than one eigenpair combining our Monte Carlo method and deflation techniques.