Recorded 25 May 2022. Robert Webber of the California Institute of Technology presents "Approximating matrix eigenvalues by subspace iteration with repeated random sparsification" at IPAM's Monte Carlo and Machine Learning Approaches in Quantum Mechanics Workshop. 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. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/workshop-iv-monte-carlo-and-machine-learning-approaches-in-quantum-mechanics/?tab=schedule