APPROXIMATING MATRIX EIGENVALUES BY SUBSPACE ITERATION WITH REPEATED RANDOM SPARSIFICATION.

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. [ABSTRACT FROM AUTHOR]