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.
Supported, in part, by the U.S. Army Research Office under Contract # DAAD19-01-1-0675
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Mascagni, M., Karaivanova, A. (2003). A Monte Carlo Approach for Finding More than One Eigenpair. In: Dimov, I., Lirkov, I., Margenov, S., Zlatev, Z. (eds) Numerical Methods and Applications. NMA 2002. Lecture Notes in Computer Science, vol 2542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36487-0_13
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DOI: https://doi.org/10.1007/3-540-36487-0_13
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