Approximating matrix eigenvalues by randomized subspace iteration

Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Randomized iterative 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 problems in quantum chemistry with matrices as large as 28 million by 28 million.