{"id":"https://openalex.org/W3012628695","doi":"https://doi.org/10.1137/19m1270367","title":"Hierarchical Matrix Approximations of Hessians Arising in Inverse Problems Governed by PDEs","display_name":"Hierarchical Matrix Approximations of Hessians Arising in Inverse Problems Governed by PDEs","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3012628695","doi":"https://doi.org/10.1137/19m1270367","mag":"3012628695"},"language":"en","primary_location":{"id":"doi:10.1137/19m1270367","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1270367","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/2003.10173","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048815529","display_name":"Ilona Ambartsumyan","orcid":"https://orcid.org/0000-0001-9268-9789"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ilona Ambartsumyan","raw_affiliation_strings":["University of Texas at Austin"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas at Austin","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088105630","display_name":"Wajih Boukaram","orcid":"https://orcid.org/0000-0002-2958-9344"},"institutions":[{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Wajih Boukaram","raw_affiliation_strings":["KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY"],"raw_orcid":"https://orcid.org/0000-0002-2958-9344","affiliations":[{"raw_affiliation_string":"KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY","institution_ids":["https://openalex.org/I71920554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008274019","display_name":"Tan Bui\u2013Thanh","orcid":"https://orcid.org/0000-0003-3002-6474"},"institutions":[{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Tan Bui-Thanh","raw_affiliation_strings":["KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY","institution_ids":["https://openalex.org/I71920554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049331711","display_name":"Omar Ghattas","orcid":"https://orcid.org/0000-0001-7742-2509"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Omar Ghattas","raw_affiliation_strings":["University of Texas at Austin"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas at Austin","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021283893","display_name":"David E. Keyes","orcid":"https://orcid.org/0000-0002-4052-7224"},"institutions":[{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"David Keyes","raw_affiliation_strings":["KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY"],"raw_orcid":"https://orcid.org/0000-0002-4052-7224","affiliations":[{"raw_affiliation_string":"KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY","institution_ids":["https://openalex.org/I71920554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012373865","display_name":"Georg Stadler","orcid":"https://orcid.org/0000-0001-7762-6544"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Georg Stadler","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066773923","display_name":"George Turkiyyah","orcid":"https://orcid.org/0000-0002-1692-5812"},"institutions":[{"id":"https://openalex.org/I98635879","display_name":"American University of Beirut","ror":"https://ror.org/04pznsd21","country_code":"LB","type":"education","lineage":["https://openalex.org/I98635879"]}],"countries":["LB"],"is_corresponding":false,"raw_author_name":"George Turkiyyah","raw_affiliation_strings":["American University of Beirut"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"American University of Beirut","institution_ids":["https://openalex.org/I98635879"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024375169","display_name":"Stefano Zampini","orcid":"https://orcid.org/0000-0002-0435-0433"},"institutions":[{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Stefano Zampini","raw_affiliation_strings":["KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY"],"raw_orcid":"https://orcid.org/0000-0002-0435-0433","affiliations":[{"raw_affiliation_string":"KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY","institution_ids":["https://openalex.org/I71920554"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5048815529"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":0.1797,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.44011463,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"42","issue":"5","first_page":"A3397","last_page":"A3426"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.9087087512016296},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5998947024345398},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5219473242759705},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.5149443745613098},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5146471261978149},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4880741834640503},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.44403427839279175},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43780848383903503},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.437583863735199},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36296942830085754},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.35301992297172546},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.348183810710907},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19534316658973694}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.9087087512016296},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5998947024345398},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5219473242759705},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.5149443745613098},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5146471261978149},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4880741834640503},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.44403427839279175},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43780848383903503},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.437583863735199},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36296942830085754},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.35301992297172546},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.348183810710907},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19534316658973694},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/19m1270367","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1270367","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2003.10173","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.10173","pdf_url":"https://arxiv.org/pdf/2003.10173","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":"mag:3012628695","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2003.10173.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:repository.kaust.edu.sa:10754/662368","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/662368","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"doi:10.48550/arxiv.2003.10173","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2003.10173","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:2003.10173","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.10173","pdf_url":"https://arxiv.org/pdf/2003.10173","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/G1346643801","display_name":null,"funder_award_id":"OSR-2018-CARF-3666","funder_id":"https://openalex.org/F4320322320","funder_display_name":"King Abdullah University of Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320322320","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3012628695.pdf","grobid_xml":"https://content.openalex.org/works/W3012628695.grobid-xml"},"referenced_works_count":75,"referenced_works":["https://openalex.org/W73123583","https://openalex.org/W140909251","https://openalex.org/W433418221","https://openalex.org/W1575501007","https://openalex.org/W1600371943","https://openalex.org/W1918112093","https://openalex.org/W1983103429","https://openalex.org/W1985588167","https://openalex.org/W1999713821","https://openalex.org/W2003017040","https://openalex.org/W2007653503","https://openalex.org/W2015356769","https://openalex.org/W2023944418","https://openalex.org/W2024165284","https://openalex.org/W2030107882","https://openalex.org/W2032117385","https://openalex.org/W2037870010","https://openalex.org/W2048369486","https://openalex.org/W2049381134","https://openalex.org/W2053225713","https://openalex.org/W2054812088","https://openalex.org/W2055631011","https://openalex.org/W2056404710","https://openalex.org/W2069383344","https://openalex.org/W2073998620","https://openalex.org/W2074836377","https://openalex.org/W2082261407","https://openalex.org/W2089958289","https://openalex.org/W2099081503","https://openalex.org/W2102074292","https://openalex.org/W2117756735","https://openalex.org/W2122137889","https://openalex.org/W2122357134","https://openalex.org/W2130350269","https://openalex.org/W2131027309","https://openalex.org/W2134373767","https://openalex.org/W2142737094","https://openalex.org/W2146961539","https://openalex.org/W2156164638","https://openalex.org/W2169370352","https://openalex.org/W2181094752","https://openalex.org/W2188296733","https://openalex.org/W2264971801","https://openalex.org/W2298381282","https://openalex.org/W2319583746","https://openalex.org/W2404865717","https://openalex.org/W2462335633","https://openalex.org/W2517666902","https://openalex.org/W2542358525","https://openalex.org/W2595059538","https://openalex.org/W2733888264","https://openalex.org/W2763634102","https://openalex.org/W2886726562","https://openalex.org/W2896757125","https://openalex.org/W2903438899","https://openalex.org/W2908511693","https://openalex.org/W2912699192","https://openalex.org/W2959257025","https://openalex.org/W2962707560","https://openalex.org/W2962841346","https://openalex.org/W2963363198","https://openalex.org/W2963441829","https://openalex.org/W2963477565","https://openalex.org/W2963863488","https://openalex.org/W2964102237","https://openalex.org/W2964186186","https://openalex.org/W2964225090","https://openalex.org/W2972598258","https://openalex.org/W3022909171","https://openalex.org/W3029645440","https://openalex.org/W3040786754","https://openalex.org/W3098146548","https://openalex.org/W3100141817","https://openalex.org/W3124464761","https://openalex.org/W4245445339"],"related_works":["https://openalex.org/W2911326131","https://openalex.org/W2262775741","https://openalex.org/W2892976100","https://openalex.org/W2604491948","https://openalex.org/W76896619","https://openalex.org/W2905865994","https://openalex.org/W2054433299","https://openalex.org/W2051965351","https://openalex.org/W3134356297","https://openalex.org/W3152462101","https://openalex.org/W2968088762","https://openalex.org/W2796807904","https://openalex.org/W2964249119","https://openalex.org/W1550477103","https://openalex.org/W3111433034","https://openalex.org/W2346348409","https://openalex.org/W2950412323","https://openalex.org/W2901087150","https://openalex.org/W1600618388","https://openalex.org/W2269135312"],"abstract_inverted_index":{"Hessian":[0,53,70],"operators":[1],"arising":[2,126],"in":[3,16,38,127],"inverse":[4,26,86,124,190],"problems":[5,125,191],"governed":[6],"by":[7,134],"partial":[8],"differential":[9],"equations":[10],"(PDEs)":[11],"play":[12],"a":[13,72,186],"critical":[14],"role":[15],"delivering":[17],"efficient,":[18],"dimension-independent":[19],"convergence":[20],"for":[21,84,122,173],"Newton":[22],"solution":[23],"of":[24,36,151,180,188,212],"deterministic":[25],"problems,":[27,87],"as":[28,30,55,89,93,113],"well":[29,132],"Markov":[31],"chain":[32],"Monte":[33],"Carlo":[34],"sampling":[35],"posteriors":[37],"the":[39,45,52,69,102,108,114,120,148],"Bayesian":[40],"setting.":[41],"These":[42],"methods":[43],"require":[44],"ability":[46],"to":[47,81,146,209,216],"repeatedly":[48],"perform":[49],"operations":[50,161],"on":[51,185],"such":[54],"multiplication":[56],"with":[57],"arbitrary":[58],"vectors,":[59],"solving":[60],"linear":[61],"systems,":[62],"inversion,":[63],"and":[64,154,159,175,182,202],"(inverse)":[65],"square":[66],"root.":[67],"Unfortunately,":[68],"is":[71,79],"(formally)":[73],"dense,":[74],"implicitly":[75],"defined":[76],"operator":[77],"that":[78,136,162],"intractable":[80],"form":[82],"explicitly":[83],"practical":[85,128],"requiring":[88],"many":[90,123],"PDE":[91],"solves":[92],"inversion":[94],"parameters.":[95],"Low":[96],"rank":[97,140,219],"approximations":[98,179],"are":[99],"effective":[100,156],"when":[101],"data":[103,115,157],"contain":[104],"limited":[105],"information":[106],"about":[107],"parameters":[109],"but":[110],"become":[111,116],"prohibitive":[112],"more":[117],"informative.":[118],"However,":[119],"Hessians":[121],"applications":[129],"can":[130],"be":[131],"approximated":[133],"matrices":[135],"have":[137,163],"hierarchically":[138],"low":[139,203,218],"structure.":[141],"Hierarchical":[142],"matrix":[143,160,178],"representations":[144,153],"promise":[145],"overcome":[147],"high":[149],"complexity":[150],"dense":[152],"provide":[155],"structures":[158],"only":[164],"log-linear":[165],"complexity.":[166],"In":[167],"this":[168],"work,":[169],"we":[170],"describe":[171],"algorithms":[172],"constructing":[174],"updating":[176],"hierarchical":[177],"Hessians,":[181],"illustrate":[183],"them":[184],"number":[187],"representative":[189],"involving":[192],"time-dependent":[193],"diffusion,":[194],"advection-dominated":[195],"transport,":[196],"frequency":[197,204],"domain":[198],"acoustic":[199],"wave":[200],"propagation,":[201],"Maxwell":[205],"equations,":[206],"demonstrating":[207],"up":[208],"an":[210],"order":[211],"magnitude":[213],"speedup":[214],"compared":[215],"globally":[217],"approximations.":[220]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
