{"id":"https://openalex.org/W2982547402","doi":"https://doi.org/10.1137/18m1194961","title":"Robust and Accurate Stopping Criteria for Adaptive Randomized Sampling in Matrix-Free Hierarchically Semiseparable Construction","display_name":"Robust and Accurate Stopping Criteria for Adaptive Randomized Sampling in Matrix-Free Hierarchically Semiseparable Construction","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2982547402","doi":"https://doi.org/10.1137/18m1194961","mag":"2982547402"},"language":"en","primary_location":{"id":"doi:10.1137/18m1194961","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1194961","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013565548","display_name":"Christopher Gorman","orcid":"https://orcid.org/0000-0002-3710-0094"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Christopher Gorman","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020496598","display_name":"Gustavo Ch\u00e1vez","orcid":"https://orcid.org/0000-0002-7593-505X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gustavo Ch\u00e1vez","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043775275","display_name":"Pieter Ghysels","orcid":"https://orcid.org/0000-0002-5981-5234"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pieter Ghysels","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065253192","display_name":"Th\u00e9o Mary","orcid":"https://orcid.org/0000-0001-9949-4634"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Th\u00e9o Mary","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046868010","display_name":"Fran\u00e7ois-Henry Rouet","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fran\u00e7ois-Henry Rouet","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5006873445","display_name":"Xiaoye Sherry Li","orcid":"https://orcid.org/0000-0002-0747-698X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaoye Sherry Li","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5013565548"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7226,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.79276815,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"41","issue":"5","first_page":"S61","last_page":"S85"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9988999962806702,"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/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/T11716","display_name":"Random Matrices and Applications","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/mathematics","display_name":"Mathematics","score":0.755933403968811},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5028290152549744},{"id":"https://openalex.org/keywords/random-projection","display_name":"Random projection","score":0.4776243567466736},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4694003164768219},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.4653032422065735},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.4637601375579834},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.4368226230144501},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.4269666373729706},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.4232936501502991},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34393996000289917},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.16174283623695374}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.755933403968811},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5028290152549744},{"id":"https://openalex.org/C2777036070","wikidata":"https://www.wikidata.org/wiki/Q18393452","display_name":"Random projection","level":2,"score":0.4776243567466736},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4694003164768219},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.4653032422065735},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.4637601375579834},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.4368226230144501},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.4269666373729706},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.4232936501502991},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34393996000289917},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.16174283623695374},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1194961","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1194961","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6859237865","display_name":null,"funder_award_id":"17-SC-20-SC","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1559275088","https://openalex.org/W1569304948","https://openalex.org/W1584657480","https://openalex.org/W1973786815","https://openalex.org/W1973915465","https://openalex.org/W1983103429","https://openalex.org/W1998187832","https://openalex.org/W2014724759","https://openalex.org/W2052087587","https://openalex.org/W2056999868","https://openalex.org/W2069914477","https://openalex.org/W2070326534","https://openalex.org/W2075490698","https://openalex.org/W2083095625","https://openalex.org/W2083903752","https://openalex.org/W2089958289","https://openalex.org/W2117756735","https://openalex.org/W2119233169","https://openalex.org/W2157237396","https://openalex.org/W2169370352","https://openalex.org/W2347093389","https://openalex.org/W2523571399","https://openalex.org/W2534273435","https://openalex.org/W2542454984","https://openalex.org/W2962760844","https://openalex.org/W2963108114"],"related_works":["https://openalex.org/W2978021564","https://openalex.org/W2057555084","https://openalex.org/W2888367694","https://openalex.org/W2018239771","https://openalex.org/W1762420609","https://openalex.org/W2134887131","https://openalex.org/W2592387312","https://openalex.org/W1634450618","https://openalex.org/W2970220474","https://openalex.org/W2077855410"],"abstract_inverted_index":{"We":[0,35,117],"present":[1],"new":[2],"algorithms":[3,19],"for":[4,56,101,132],"randomized":[5,25],"construction":[6,18],"of":[7,48,72,75,83,105,109,113,126,135,154],"hierarchically":[8],"semiseparable":[9],"(HSS)":[10],"matrices,":[11,146],"addressing":[12],"several":[13],"practical":[14],"issues.":[15],"The":[16,90],"HSS":[17],"use":[20],"a":[21,87,133],"partially":[22],"matrix-free,":[23],"adaptive":[24],"projection":[26,51,108],"scheme":[27],"to":[28,43,63],"determine":[29,44],"the":[30,45,49,66,73,81,102,106,110,114,148,155],"maximum":[31],"off-diagonal":[32],"block":[33],"rank.":[34],"develop":[36],"both":[37,127],"relative":[38,91],"and":[39,78,92,121,123,142,151],"absolute":[40,93],"stopping":[41,94],"criteria":[42,95],"minimum":[46],"dimension":[47],"random":[50,67,76,84,107],"matrix":[52],"that":[53],"is":[54],"sufficient":[55],"desired":[57],"accuracy.":[58],"Two":[59],"strategies":[60],"are":[61,96],"discussed":[62],"adaptively":[64],"enlarge":[65],"sample":[68],"matrix:":[69],"repeated":[70],"doubling":[71],"number":[74,82],"vectors":[77,85],"iteratively":[79],"incrementing":[80],"by":[86],"fixed":[88],"number.":[89],"based":[97],"on":[98],"probabilistic":[99],"bounds":[100],"Frobenius":[103],"norm":[104],"Hankel":[111],"blocks":[112],"input":[115],"matrix.":[116],"discuss":[118],"parallel":[119],"implementation":[120],"computation":[122],"communication":[124],"cost":[125],"variants.":[128],"Parallel":[129],"numerical":[130,152],"results":[131],"range":[134],"applications,":[136],"including":[137],"boundary":[138],"element":[139],"method":[140],"matrices":[141],"quantum":[143],"chemistry":[144],"Toeplitz":[145],"show":[147],"effectiveness,":[149],"scalability,":[150],"robustness":[153],"proposed":[156],"algorithms.":[157]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
