Approximating matrix eigenvalues by subspace iteration with repeated random sparsification

TL;DR

This paper introduces an extension of iterative random sparsification methods to estimate multiple eigenvalues of large matrices efficiently, demonstrated through quantum chemistry benchmarks.

Contribution

It presents a novel approach to extend random sparsification techniques for estimating multiple eigenvalues, improving computational efficiency for high-dimensional matrices.

Findings

Effective estimation of multiple eigenvalues demonstrated

Reduced computational cost compared to traditional methods

Successful application to quantum chemistry problems

Abstract

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.