@article{1d85711897354e0bb36064396405c92f,
title = "APPROXIMATING MATRIX EIGENVALUES BY SUBSPACE ITERATION WITH REPEATED RANDOM SPARSIFICATION",
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.",
keywords = "Monte Carlo, eigenvalues, randomized algorithms, subspace iteration",
author = "Greene, {Samuel M.} and Webber, {Robert J.} and Berkelbach, {Timothy C.} and Jonathan Weare",
note = "Funding Information: \ast Submitted to the journal's Methods and Algorithms for Scientific Computing section May 25, 2021; accepted for publication (in revised form) May 9, 2022; published electronically September 26, 2022. https://doi.org/10.1137/21M1422513 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : The work of the first author was supported by an investment fellowship from the Molecular Sciences Software Institute, which is funded by U.S. National Science Foundation grant OAC-1547580. The work of the second author was supported by New York University's Dean's Dissertation Fellowship and by the National Science Foundation through award DMS-1646339. The work of the fourth author was supported by the Advanced Scientific Computing Research Program within the DOE Office of Science through award DE-SC0020427. The Flatiron Institute is a division of the Simons Foundation. Funding Information: The work of the first author was supported by an investment fellowship from the Molecular Sciences Software Institute, which is funded by U.S. National Science Foundation grant OAC-1547580. The work of the second author was supported by New York University's Dean's Dissertation Fellowship and by the National Science Foundation through award DMS-1646339. The work of the fourth author was supported by the Advanced Scientific Computing Research Program within the DOE Office of Science through award DE-SC0020427. The Flatiron Institute is a division of the Simons Foundation. We gratefully acknowledge productive discussions with Aaron Dinner, Michael Lindsey, Verena Neufeld, Joel Tropp, Ethan Epperly, and James Smith throughout the development and execution of this project. Lek-Heng Lim originally raised the possibility of randomizing subspace iteration to us. Benjamin Pritchard provided invaluable suggestions for improving the readability and efficiency of our source code. Computational resources were provided by the Research Computing Center at the University of Chicago and the High Performance Computing Center at New York University. Publisher Copyright: {\textcopyright} 2022 SIAM.",
year = "2022",
doi = "10.1137/21M1422513",
language = "English (US)",
volume = "44",
journal = "SIAM Journal on Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "5",
}