{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:47:36Z","timestamp":1776836856995,"version":"3.51.2"},"reference-count":68,"publisher":"American Mathematical Society (AMS)","issue":"342","license":[{"start":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T00:00:00Z","timestamp":1709078400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1953120"],"award-info":[{"award-number":["1953120"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1953120"],"award-info":[{"award-number":["1953120"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1953120"],"award-info":[{"award-number":["1953120"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1953120"],"award-info":[{"award-number":["1953120"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>The convergence property of a stochastic algorithm for the self-consistent field (SCF) calculations of electron structures is studied. The algorithm is formulated by rewriting the electronic charges as a trace\/diagonal of a matrix function, which is subsequently expressed as a statistical average. The function is further approximated by using a Krylov subspace approximation. As a result, each SCF iteration only samples one random vector without having to compute all the orbitals. We consider the common practice of SCF iterations with damping and mixing. We prove that the iterates from a general linear mixing scheme converge in a probabilistic sense when the stochastic error has a second finite moment.<\/p>","DOI":"10.1090\/mcom\/3826","type":"journal-article","created":{"date-parts":[[2023,1,25]],"date-time":"2023-01-25T09:18:06Z","timestamp":1674638286000},"page":"1693-1728","source":"Crossref","is-referenced-by-count":4,"title":["Stochastic algorithms for self-consistent calculations of electronic structures"],"prefix":"10.1090","volume":"92","author":[{"given":"Taehee","family":"Ko","sequence":"first","affiliation":[]},{"given":"Xiantao","family":"Li","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2023,2,28]]},"reference":[{"issue":"12","key":"1","doi-asserted-by":"crossref","first-page":"2123","DOI":"10.4236\/am.2012.312A293","article-title":"Stochastic approximation method for fixed point problems","volume":"3","author":"Alber, Y. I.","year":"2012","journal-title":"Appl. Math."},{"issue":"2","key":"2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1944345.1944349","article-title":"Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix","volume":"58","author":"Avron, H.","year":"2011","journal-title":"J.~ACM","ISSN":"https:\/\/id.crossref.org\/issn\/0004-5411","issn-type":"print"},{"key":"3","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.cplett.2016.01.033","article-title":"Periodic pulay method for robust and efficient convergence acceleration of self-consistent field iterations","volume":"647","author":"Banerjee, A. S.","year":"2016","journal-title":"Chem.\\ Phys.\\ Lett."},{"issue":"4","key":"4","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1103\/RevModPhys.72.1041","article-title":"Real-space mesh techniques in density-functional theory","volume":"72","author":"Beck, T. L.","year":"2000","journal-title":"Rev.\\ Mod.\\ Phys."},{"issue":"11-12","key":"5","doi-asserted-by":"publisher","first-page":"1214","DOI":"10.1016\/j.apnum.2007.01.003","article-title":"An estimator for the diagonal of a matrix","volume":"57","author":"Bekas, C.","year":"2007","journal-title":"Appl. Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0168-9274","issn-type":"print"},{"key":"6","series-title":"Advances in Neural Information Processing Systems","volume-title":"The Tradeoffs of Large Scale Learning","volume":"20","author":"Bottou, L.","year":"2007"},{"issue":"2","key":"7","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1137\/16M1080173","article-title":"Optimization methods for large-scale machine learning","volume":"60","author":"Bottou, L\u00e9on","year":"2018","journal-title":"SIAM Rev.","ISSN":"https:\/\/id.crossref.org\/issn\/1095-7200","issn-type":"print"},{"issue":"4","key":"8","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1016\/S0009-2614(00)00750-8","article-title":"An efficient and robust technique for achieving self consistency in electronic structure calculations","volume":"325","author":"Bowler, D. R.","year":"2000","journal-title":"Chem.\\ Phys.\\ Lett."},{"issue":"11","key":"9","first-page":"2781","article-title":"Recent progress in linear scaling ab initio electronic structure techniques","volume":"14","author":"Bowler, D. R.","year":"2002","journal-title":"J.~Phys."},{"issue":"24","key":"10","doi-asserted-by":"crossref","first-page":"10616","DOI":"10.1063\/1.1373430","article-title":"Self-consistent field algorithms for Kohn\u2013Sham models with fractional occupation numbers","volume":"114","author":"Canc\u00e8s, E.","year":"2001","journal-title":"J. Chem. Phys."},{"issue":"1","key":"11","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1137\/20M1332864","article-title":"Convergence analysis of direct minimization and self-consistent iterations","volume":"42","author":"Canc\u00e8s, \u00c9ric","year":"2021","journal-title":"SIAM J. Matrix Anal. Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0895-4798","issn-type":"print"},{"issue":"2","key":"12","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1002\/1097-461X(2000)79:2<82::AID-QUA3>3.0.CO;2-I","article-title":"Can we outperform the DIIS approach for electronic structure calculations?","volume":"79","author":"Canc\u00e8s, E.","year":"2000","journal-title":"Int.\\ J.~Quantum Chem."},{"issue":"4","key":"13","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1051\/m2an:2000102","article-title":"On the convergence of SCF algorithms for the Hartree-Fock equations","volume":"34","author":"Canc\u00e8s, Eric","year":"2000","journal-title":"M2AN Math. Model. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-583X","issn-type":"print"},{"key":"14","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1214\/aoms\/1177728716","article-title":"On a stochastic approximation method","volume":"25","author":"Chung, K. L.","year":"1954","journal-title":"Ann. Math. Statistics","ISSN":"https:\/\/id.crossref.org\/issn\/0003-4851","issn-type":"print"},{"issue":"11","key":"15","doi-asserted-by":"crossref","first-page":"115207","DOI":"10.1103\/PhysRevB.97.115207","article-title":"Stochastic density functional theory at finite temperatures","volume":"97","author":"Cytter, Y.","year":"2018","journal-title":"Phys.\\ Rev.\\ B"},{"key":"16","article-title":"Saga: A fast incremental gradient method with support for non-strongly convex composite objectives","author":"Defazio, A.","year":"2014","journal-title":"arXiv preprint \\arXiv{1407.0202}"},{"issue":"4","key":"17","doi-asserted-by":"publisher","first-page":"1546","DOI":"10.1137\/070688924","article-title":"Error estimates for polynomial Krylov approximations to matrix functions","volume":"30","author":"Diele, Fasma","year":"2008","journal-title":"SIAM J. Matrix Anal. Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0895-4798","issn-type":"print"},{"issue":"6","key":"18","doi-asserted-by":"publisher","first-page":"2481","DOI":"10.1137\/050633846","article-title":"A restarted Krylov subspace method for the evaluation of matrix functions","volume":"44","author":"Eiermann, Michael","year":"2006","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"11","key":"19","doi-asserted-by":"crossref","first-page":"7260","DOI":"10.1103\/PhysRevB.58.7260","article-title":"Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties","volume":"58","author":"Elstner, M.","year":"1998","journal-title":"Phys. Rev. B"},{"issue":"3","key":"20","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1002\/nla.617","article-title":"Two classes of multisecant methods for nonlinear acceleration","volume":"16","author":"Fang, Haw-ren","year":"2009","journal-title":"Numer. Linear Algebra Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/1070-5325","issn-type":"print"},{"issue":"4","key":"21","doi-asserted-by":"publisher","first-page":"999","DOI":"10.4310\/cms.2007.v5.n4.a14","article-title":"A sub-linear scaling algorithm for computing the electronic structure of materials","volume":"5","author":"Garc\u00eda-Cervera, Carlos J.","year":"2007","journal-title":"Commun. Math. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/1539-6746","issn-type":"print"},{"issue":"4","key":"22","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1103\/RevModPhys.71.1085","article-title":"Linear scaling electronic structure methods","volume":"71","author":"Goedecker, S.","year":"1999","journal-title":"Rev. Mod. Phys."},{"key":"23","article-title":"The random batch method for \ud835\udc41-Body quantum dynamics","author":"Golse, F.","year":"2019","journal-title":"arXiv preprint \\arXiv{1912.07424}"},{"issue":"10","key":"24","doi-asserted-by":"crossref","first-page":"5728","DOI":"10.1063\/1.449880","article-title":"Direct inversion in the iterative subspace (DIIS) optimization of open-shell, excited-state, and small multiconfiguration scf wave functions","volume":"84","author":"Hamilton, T. P.","year":"1986","journal-title":"J.\\ Chem. Phys."},{"issue":"10","key":"25","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1038\/s41557-020-0544-y","article-title":"Deep-neural-network solution of the electronic Schr\u00f6dinger equation","volume":"12","author":"Hermann, J.","year":"2020","journal-title":"Nat.\\ Chem."},{"key":"26","doi-asserted-by":"crossref","first-page":"B864--B871","DOI":"10.1103\/PhysRev.136.B864","article-title":"Inhomogeneous electron gas","volume":"136","author":"Hohenberg, P.","year":"1964","journal-title":"Phys. Rev. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0031-899X","issn-type":"print"},{"issue":"5","key":"27","doi-asserted-by":"publisher","first-page":"1907","DOI":"10.4208\/cicp.oa-2020-0168","article-title":"Random batch algorithms for quantum Monte Carlo simulations","volume":"28","author":"Jin, Shi","year":"2020","journal-title":"Commun. Comput. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/1815-2406","issn-type":"print"},{"issue":"18","key":"28","doi-asserted-by":"crossref","first-page":"12807","DOI":"10.1103\/PhysRevB.38.12807","article-title":"Modified Broyden\u2019s method for accelerating convergence in self-consistent calculations","volume":"38","author":"Johnson, D. D.","year":"1988","journal-title":"Phys.\\ Rev.\\ B"},{"key":"29","series-title":"Advances in Neural Information Processing Systems","volume-title":"Accelerating Stochastic Gradient Descent Using Predictive Variance Reduction","volume":"26","author":"Johnson, R.","year":"2013"},{"key":"30","volume-title":"Numerical analysis: mathematics of scientific computing","volume":"2","author":"Kincaid, D.","year":"2009"},{"key":"31","doi-asserted-by":"crossref","first-page":"A1133--A1138","DOI":"10.1103\/PhysRev.140.A1133","article-title":"Self-consistent equations including exchange and correlation effects","volume":"140","author":"Kohn, W.","year":"1965","journal-title":"Phys. Rev. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0031-899X","issn-type":"print"},{"issue":"16","key":"32","doi-asserted-by":"crossref","first-page":"11169","DOI":"10.1103\/PhysRevB.54.11169","article-title":"Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set","volume":"54","author":"Kresse, G.","year":"1996","journal-title":"Phys.\\ Rev.\\ B"},{"issue":"5","key":"33","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1002\/pssb.200541463","article-title":"PARSEC\u2013the pseudopotential algorithm for real-space electronic structure calculations: recent advances and novel applications to nano-structures","volume":"243","author":"Kronik, L.","year":"2006","journal-title":"Phys. Status Solidi (b)"},{"key":"34","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1073\/pnas.53.1.8","article-title":"On the stability of stochastic dynamical systems","volume":"53","author":"Kushner, Harold J.","year":"1965","journal-title":"Proc. Nat. Acad. Sci. U.S.A.","ISSN":"https:\/\/id.crossref.org\/issn\/0027-8424","issn-type":"print"},{"key":"35","series-title":"Mathematics in Science and Engineering, Vol. 33","volume-title":"Stochastic stability and control","author":"Kushner, Harold J.","year":"1967"},{"key":"36","series-title":"Applications of Mathematics (New York)","isbn-type":"print","volume-title":"Stochastic approximation and recursive algorithms and applications","volume":"35","author":"Kushner, Harold J.","year":"2003","ISBN":"https:\/\/id.crossref.org\/isbn\/0387008942","edition":"2"},{"key":"37","volume-title":"Applied stochastic processes","author":"Lefebvre, M.","year":"2007"},{"issue":"1","key":"38","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1137\/130934283","article-title":"Approximating spectral densities of large matrices","volume":"58","author":"Lin, L.","year":"2016","journal-title":"SIAM Rev."},{"issue":"5","key":"39","doi-asserted-by":"publisher","first-page":"S277--S298","DOI":"10.1137\/120880604","article-title":"Elliptic preconditioner for accelerating the self-consistent field iteration in Kohn-Sham density functional theory","volume":"35","author":"Lin, Lin","year":"2013","journal-title":"SIAM J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/1064-8275","issn-type":"print"},{"issue":"1","key":"40","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/S0010-4655(02)00686-0","article-title":"octopus: a first-principles tool for excited electron\u2013ion dynamics","volume":"151","author":"Marques, M. A.","year":"2003","journal-title":"Comp.\\ Phys.\\ Commun."},{"key":"41","volume-title":"{Electronic Structure: Basic Theory and Practical Methods}","author":"Martin, R. M.","year":"2011"},{"key":"42","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1017\/s0962492920000021","article-title":"Randomized numerical linear algebra: foundations and algorithms","volume":"29","author":"Martinsson, Per-Gunnar","year":"2020","journal-title":"Acta Numer.","ISSN":"https:\/\/id.crossref.org\/issn\/0962-4929","issn-type":"print"},{"key":"43","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511609633","volume-title":"Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods","author":"Marx, D.","year":"2009"},{"key":"44","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719512","volume-title":"Matrix analysis and applied linear algebra","author":"Meyer, Carl","year":"2000","ISBN":"https:\/\/id.crossref.org\/isbn\/0898714540"},{"key":"45","doi-asserted-by":"crossref","DOI":"10.1063\/5.0053674","article-title":"Frontiers of Stochastic Electronic Structure Calculations","author":"Morales-Silva, M. A.","year":"2021"},{"key":"46","first-page":"2613","article-title":"Sarah: A novel method for machine learning problems using stochastic recursive gradient","author":"Nguyen, L. M.","year":"2017"},{"key":"47","series-title":"Cambridge Series in Statistical and Probabilistic Mathematics","isbn-type":"print","volume-title":"Markov chains","volume":"2","author":"Norris, J. R.","year":"1998","ISBN":"https:\/\/id.crossref.org\/isbn\/0521481813"},{"key":"48","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195092769.001.0001","volume-title":"Density-Functional Theory of Atoms and Molecules","author":"Parr, R. G.","year":"1995"},{"issue":"4","key":"49","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.1103\/RevModPhys.64.1045","article-title":"Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients","volume":"64","author":"Payne, M. C.","year":"1992","journal-title":"Rev.\\ Mod.\\ Phys."},{"key":"50","first-page":"314","article-title":"Stochastic Variance Reduction for Nonconvex Optimization","author":"Reddi, S. J.","year":"2016"},{"key":"51","series-title":"Modern Birkh\\\"{a}user Classics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-8409-9","volume-title":"A probability path","author":"Resnick, Sidney I.","year":"2014","ISBN":"https:\/\/id.crossref.org\/isbn\/9780817684082"},{"issue":"11","key":"52","doi-asserted-by":"crossref","first-page":"5593","DOI":"10.1063\/1.443766","article-title":"Fixed-node quantum Monte Carlo for molecules","volume":"77","author":"Reynolds, P. J.","year":"1982","journal-title":"J.~Chem.\\ Phys."},{"key":"53","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1214\/aoms\/1177729586","article-title":"A stochastic approximation method","volume":"22","author":"Robbins, Herbert","year":"1951","journal-title":"Ann. Math. Statistics","ISSN":"https:\/\/id.crossref.org\/issn\/0003-4851","issn-type":"print"},{"issue":"1","key":"54","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1137\/0729014","article-title":"Analysis of some Krylov subspace approximations to the matrix exponential operator","volume":"29","author":"Saad, Y.","year":"1992","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"11","key":"55","first-page":"2745","article-title":"The SIESTA method for ab initio order-N materials simulation","volume":"14","author":"Soler, J. M.","year":"2002","journal-title":"J.~Phys."},{"issue":"2","key":"56","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1016\/j.jmps.2009.10.002","article-title":"Non-periodic finite-element formulation of Kohn-Sham density functional theory","volume":"58","author":"Suryanarayana, Phanish","year":"2010","journal-title":"J. Mech. Phys. Solids","ISSN":"https:\/\/id.crossref.org\/issn\/0022-5096","issn-type":"print"},{"key":"57","isbn-type":"print","volume-title":"Accelerating the Computation of Density Functional Theory's Correlation Energy under Random Phase Approximations","author":"Thicke, Kyle","year":"2019","ISBN":"https:\/\/id.crossref.org\/isbn\/9781088333891"},{"issue":"5","key":"58","doi-asserted-by":"publisher","first-page":"S47--S65","DOI":"10.1137\/16M1080677","article-title":"Local improvement results for Anderson acceleration with inaccurate function evaluations","volume":"39","author":"Toth, Alex","year":"2017","journal-title":"SIAM J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/1064-8275","issn-type":"print"},{"issue":"2","key":"59","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1137\/130919398","article-title":"Convergence analysis for Anderson acceleration","volume":"53","author":"Toth, Alex","year":"2015","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"60","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611975949","volume-title":"Approximation theory and approximation practice, extended edition","author":"Trefethen, L. N.","year":"2019"},{"issue":"50","key":"61","first-page":"R1297","article-title":"Ab initio molecular dynamics: basic concepts, current trends and novel applications","volume":"14","author":"Tuckerman, M. E.","year":"2002","journal-title":"J.~Phys."},{"issue":"11","key":"62","doi-asserted-by":"publisher","first-page":"1432","DOI":"10.1002\/cpa.20330","article-title":"Electronic structure of smoothly deformed crystals: Cauchy-Born rule for the nonlinear tight-binding model","volume":"63","author":"E, Weinan","year":"2010","journal-title":"Comm. Pure Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-3640","issn-type":"print"},{"key":"63","series-title":"Cambridge Mathematical Textbooks","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511813658","volume-title":"Probability with martingales","author":"Williams, David","year":"1991","ISBN":"https:\/\/id.crossref.org\/isbn\/052140455X"},{"key":"64","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1214\/aoms\/1177729391","article-title":"On the stochastic approximation method of Robbins and Monro","volume":"23","author":"Wolfowitz, J.","year":"1952","journal-title":"Ann. Math. Statistics","ISSN":"https:\/\/id.crossref.org\/issn\/0003-4851","issn-type":"print"},{"issue":"4","key":"65","doi-asserted-by":"publisher","first-page":"A2749--A2773","DOI":"10.1137\/17M1135542","article-title":"Fast computation of spectral densities for generalized eigenvalue problems","volume":"40","author":"Xi, Yuanzhe","year":"2018","journal-title":"SIAM J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/1064-8275","issn-type":"print"},{"issue":"2","key":"66","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1016\/j.jcp.2006.01.030","article-title":"A constrained optimization algorithm for total energy minimization in electronic structure calculations","volume":"217","author":"Yang, Chao","year":"2006","journal-title":"J. Comput. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9991","issn-type":"print"},{"issue":"3","key":"67","doi-asserted-by":"publisher","first-page":"C265--C289","DOI":"10.1137\/130932934","article-title":"Gradient type optimization methods for electronic structure calculations","volume":"36","author":"Zhang, Xin","year":"2014","journal-title":"SIAM J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/1064-8275","issn-type":"print"},{"issue":"1","key":"68","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.jcp.2006.03.017","article-title":"Self-consistent-field calculations using chebyshev-filtered subspace iteration","volume":"219","author":"Zhou, Y.","year":"2006","journal-title":"J.~Comput.\\ Phys."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/mcom\/2023-92-342\/S0025-5718-2023-03826-1\/mcom3826_AM.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/www.ams.org\/mcom\/2023-92-342\/S0025-5718-2023-03826-1\/S0025-5718-2023-03826-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:58:17Z","timestamp":1776833897000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2023-92-342\/S0025-5718-2023-03826-1\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,28]]},"references-count":68,"journal-issue":{"issue":"342","published-print":{"date-parts":[[2023,7]]}},"alternative-id":["S0025-5718-2023-03826-1"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3826","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2023,2,28]]}}}