Abstract
A Monte-Carlo approach for solving huge, dense matrices for eigenvalues and eigenvectors is proposed. The matrix must satisfy certain conditions including a smooth density of diagonal elements curve and relatively constant off-diagonal elements. The approach simply involves randomly choosing a finite order (as large as computationally possible) subset matrix from the original matrix and then diagonalizing the subset. The results are crude, but often informative.
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Groh, D.J., Marshall, R.A., Kunz, A.B. et al. An approximation method for eigenvectors of very large matrices. J Sci Comput 6, 251–267 (1991). https://doi.org/10.1007/BF01062812
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DOI: https://doi.org/10.1007/BF01062812