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APPROXIMATING MATRIX EIGENVALUES BY SUBSPACE ITERATION WITH REPEATED RANDOM SPARSIFICATION
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DOI：10.1137/21M1422513.png)
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Abstract
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Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Iterative random sparsification methods allow for the estimation of a single dominant eigenvalue at reduced cost by leveraging repeated random sampling and averaging. We present a general approach to extending such methods for the estimation of multiple eigenvalues and demonstrate its performance for several benchmark problems in quantum chemistry.
Keywords:
eigenvalues
subspace iteration
randomized algorithms
Monte Carlo
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