{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:29:53Z","timestamp":1787336993368,"version":"build-2736575974"},"reference-count":37,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1606277"],"award-info":[{"award-number":["DMS-1606277"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1328230"],"award-info":[{"award-number":["DMS-1328230"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1521830"],"award-info":[{"award-number":["DMS-1521830"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-FC02-13ER26134\/DE-SC0009409"],"award-info":[{"award-number":["DE-FC02-13ER26134\/DE-SC0009409"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>Localized representation of the Kohn--Sham subspace plays an important role in quantum chemistry and materials science. The recently developed selected columns of the density matrix (SCDM) method [A. Damle, L. Lin, and L. Ying, J. Chem. Theory Comput., 11 (2015), pp. 1463--1469}] is a simple and robust procedure for finding a localized representation of a set of Kohn--Sham orbitals from an insulating system. The SCDM method allows the direct construction of a well conditioned (or even orthonormal) and localized basis for the Kohn--Sham subspace. The SCDM algorithm avoids the use of an optimization procedure and does not depend on any adjustable parameters. The most computationally expensive step of the SCDM method is a column pivoted QR factorization that identifies the important columns for constructing the localized basis set. In this paper, we develop a two-stage approximate column selection strategy to find the important columns at much lower computational cost. We demonstrate the effectiveness of this process using the dissociation process of a BH$_{3}$NH$_{3}$ molecule, an alkane chain, and a supercell with $256$ water molecules. Numerical results for the large collection of water molecules show that the two-stage localization procedure can be more than 30 times faster than the original SCDM algorithm and compares favorably with the popular Wannier90 package.<\/jats:p>","DOI":"10.1137\/16m1098589","type":"journal-article","created":{"date-parts":[[2017,12,12]],"date-time":"2017-12-12T13:39:33Z","timestamp":1513085973000},"page":"B1178-B1198","source":"Crossref","is-referenced-by-count":11,"title":["Computing Localized Representations of the Kohn--Sham Subspace Via Randomization and Refinement"],"prefix":"10.1137","volume":"39","author":[{"given":"Anil","family":"Damle","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lin","family":"Lin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lexing","family":"Ying","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,12,12]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719604"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1063\/1.2360264"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1063\/1.464913"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/100814019"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719642"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/S0081-1947(08)60459-2"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.98.046402"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.135.A698"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.135.A685"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1021\/ct500985f"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2016.12.053"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"J. Demmel, L. Grigori, M. Gu, and H. Xiang,\n                      Communication Avoiding Rank Revealing QR Factorization with Column Pivoting\n                      , Tech. Report UCB\/EECS-2013-46, EECS Department, University of California, Berkeley, 2013.","DOI":"10.21236\/ADA584728"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/15M1044680"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0913345107"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.32.300"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1088\/0953-8984\/21\/39\/395502"},{"key":"atypb17","volume-title":"Matrix Computations","author":"Golub G. 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