{"id":"https://openalex.org/W4403241467","doi":"https://doi.org/10.1137/24m1700697","title":"A Posteriori Error Estimates for Schr\u00f6dinger Operators Discretized with Linear Combinations of Atomic Orbitals","display_name":"A Posteriori Error Estimates for Schr\u00f6dinger Operators Discretized with Linear Combinations of Atomic Orbitals","publication_year":2025,"publication_date":"2025-12-16","ids":{"openalex":"https://openalex.org/W4403241467","doi":"https://doi.org/10.1137/24m1700697"},"language":"en","primary_location":{"id":"doi:10.1137/24m1700697","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1700697","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2410.04943","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Mi-Song Dupuy","orcid":null},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]},{"id":"https://openalex.org/I4387152972","display_name":"Laboratoire de Math\u00e9matiques de Besan\u00e7on","ror":"https://ror.org/04nrhwg12","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4387152972","https://openalex.org/I4405256580"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Mi-Song Dupuy","raw_affiliation_strings":["Laboratoire Jacques-Louis Lions, Sorbonne Universit\u00e9, Paris, France","LMB - Laboratoire de Math\u00e9matiques de Besan\u00e7on (UMR 6623) (UFR Sciences et techniques 16 route de Gray 25 030 Besan\u00e7on cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions, Sorbonne Universit\u00e9, Paris, France","institution_ids":["https://openalex.org/I4210158291","https://openalex.org/I39804081"]},{"raw_affiliation_string":"LMB - Laboratoire de Math\u00e9matiques de Besan\u00e7on (UMR 6623) (UFR Sciences et techniques 16 route de Gray 25 030 Besan\u00e7on cedex - France)","institution_ids":["https://openalex.org/I4387152972"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051564846","display_name":"Genevi\u00e8ve Dusson","orcid":"https://orcid.org/0000-0002-7160-6064"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4405256580","display_name":"Universit\u00e9 Marie et Louis Pasteur","ror":"https://ror.org/04asdee31","country_code":"FR","type":"education","lineage":["https://openalex.org/I4405256580"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Genevi\u00e8ve Dusson","raw_affiliation_strings":["Universit\u00e9 Marie et Louis Pasteur, CNRS, LmB (UMR 6623), F-25000 Besan\u00e7on, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Marie et Louis Pasteur, CNRS, LmB (UMR 6623), F-25000 Besan\u00e7on, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4405256580"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107113959","display_name":"Ioanna-Maria Lygatsika","orcid":null},"institutions":[{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210101455","display_name":"CEA DAM \u00cele-de-France","ror":"https://ror.org/00kn4eb29","country_code":"FR","type":"government","lineage":["https://openalex.org/I4210101455"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ioanna-Maria Lygatsika","raw_affiliation_strings":["CEA DAM-DIF, F-91297 Arpajon, France; and Universit\u00e9 Paris-Saclay, CEA, LMCE, F-91680, Laboratoire Mati\u00e8re en Conditions Extr\u00eames, 91680 Bruy\u00e8res-le-Ch\u00e2tel, France","CEA/DAM - CEA/DAM [Arpajon] (2 Rue de la Piquetterie\r\n91680 Bruy\u00e8res-le-Ch\u00e2tel - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CEA DAM-DIF, F-91297 Arpajon, France; and Universit\u00e9 Paris-Saclay, CEA, LMCE, F-91680, Laboratoire Mati\u00e8re en Conditions Extr\u00eames, 91680 Bruy\u00e8res-le-Ch\u00e2tel, France","institution_ids":["https://openalex.org/I277688954","https://openalex.org/I2738703131","https://openalex.org/I4210101455"]},{"raw_affiliation_string":"CEA/DAM - CEA/DAM [Arpajon] (2 Rue de la Piquetterie\r\n91680 Bruy\u00e8res-le-Ch\u00e2tel - France)","institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I4210101455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291","https://openalex.org/I4387152972"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01508349,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"63","issue":"6","first_page":"2395","last_page":"2420"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/atomic-orbital","display_name":"Atomic orbital","score":0.5944119095802307},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5923914313316345},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5724737644195557},{"id":"https://openalex.org/keywords/schr\u00f6dingers-cat","display_name":"Schr\u00f6dinger's cat","score":0.4669310450553894},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4656665325164795},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44828665256500244},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3762284815311432},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3071025013923645},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.29336732625961304},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22439700365066528},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.07425332069396973}],"concepts":[{"id":"https://openalex.org/C189394030","wikidata":"https://www.wikidata.org/wiki/Q53860","display_name":"Atomic orbital","level":3,"score":0.5944119095802307},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5923914313316345},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5724737644195557},{"id":"https://openalex.org/C194800363","wikidata":"https://www.wikidata.org/wiki/Q8588","display_name":"Schr\u00f6dinger's cat","level":2,"score":0.4669310450553894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4656665325164795},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44828665256500244},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3762284815311432},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3071025013923645},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.29336732625961304},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22439700365066528},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.07425332069396973},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/24m1700697","is_oa":false,"landing_page_url":"https://doi.org/10.1137/24m1700697","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2410.04943","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2410.04943","pdf_url":"https://arxiv.org/pdf/2410.04943","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-04723742v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04723742","pdf_url":"https://hal.science/hal-04723742/document","source":{"id":"https://openalex.org/S4406922454","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2024","raw_type":"Preprints, Working Papers, ..."},{"id":"doi:10.48550/arxiv.2410.04943","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2410.04943","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2410.04943","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2410.04943","pdf_url":"https://arxiv.org/pdf/2410.04943","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2361257913","display_name":null,"funder_award_id":"810367","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2609535829","display_name":null,"funder_award_id":"2023-2025","funder_id":"https://openalex.org/F4320330232","funder_display_name":"Sorbonne Universit\u00e9"},{"id":"https://openalex.org/G734872842","display_name":null,"funder_award_id":"15-IDEX-0003","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7683707404","display_name":null,"funder_award_id":"810367","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7831147273","display_name":"Extreme-scale Mathematically-based Computational Chemistry","funder_award_id":"810367","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G812171912","display_name":null,"funder_award_id":"ANR-15-IDEX-0003","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320330232","display_name":"Sorbonne Universit\u00e9","ror":null},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403241467.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2793786119","https://openalex.org/W1507702947","https://openalex.org/W2022062253"],"abstract_inverted_index":{"We":[0,30,89],"establish":[1],"guaranteed":[2],"and":[3,13,114],"practically":[4],"computable":[5],"a":[6,98],"posteriori":[7,99],"error":[8,39,59,108,118],"bounds":[9,109],"for":[10,121],"source":[11],"problems":[12,15],"eigenvalue":[14],"involving":[16],"linear":[17,25],"Schr{\u00f6}dinger":[18,80],"operators":[19,81],"with":[20,24],"atom-centered":[21],"potentials":[22],"discretized":[23],"combinations":[26],"of":[27,36,48,70,74,93,96],"atomic":[28,55,75],"orbitals.":[29],"show":[31,65],"that":[32,51,66,106,115],"the":[33,37,44,49,58,67,71,94,107,112,116],"energy":[34,46],"norm":[35,47],"discretization":[38],"can":[40,83],"be":[41,85],"estimated":[42],"by":[43],"dual":[45,72],"residual,":[50],"further":[52],"decomposes":[53],"into":[54],"contributions,":[56],"characterizing":[57],"localized":[60,117],"on":[61,101],"atoms.":[62],"Moreover,":[63],"we":[64],"practical":[68],"computation":[69],"norms":[73],"residuals":[76],"involves":[77],"diagonalizing":[78],"radial":[79],"which":[82],"easily":[84],"precomputed":[86],"in":[87],"practice.":[88],"provide":[90],"numerical":[91],"illustrations":[92],"performance":[95],"such":[97],"analysis":[100],"several":[102],"test":[103],"cases,":[104],"showing":[105],"accurately":[110],"estimate":[111],"error,":[113],"components":[119],"allow":[120],"optimized":[122],"adaptive":[123],"basis":[124],"sets.":[125]},"counts_by_year":[],"updated_date":"2026-05-04T08:30:34.212998","created_date":"2024-10-10T00:00:00"}
