{"id":"https://openalex.org/W2615262195","doi":"https://doi.org/10.1080/10556788.2020.1725751","title":"An investigation of Newton-Sketch and subsampled Newton methods","display_name":"An investigation of Newton-Sketch and subsampled Newton methods","publication_year":2020,"publication_date":"2020-02-12","ids":{"openalex":"https://openalex.org/W2615262195","doi":"https://doi.org/10.1080/10556788.2020.1725751","mag":"2615262195"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2020.1725751","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2020.1725751","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/1705.06211","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029030164","display_name":"Albert S. Berahas","orcid":"https://orcid.org/0000-0002-2371-9398"},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Albert S. Berahas","raw_affiliation_strings":["Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA","Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA#TAB#"],"raw_orcid":"https://orcid.org/0000-0002-2371-9398","affiliations":[{"raw_affiliation_string":"Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA","institution_ids":["https://openalex.org/I186143895"]},{"raw_affiliation_string":"Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA#TAB#","institution_ids":["https://openalex.org/I186143895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083156016","display_name":"Raghu Bollapragada","orcid":null},"institutions":[{"id":"https://openalex.org/I1282105669","display_name":"Argonne National Laboratory","ror":"https://ror.org/05gvnxz63","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282105669","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Raghu Bollapragada","raw_affiliation_strings":["Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL, USA","Northwestern University"],"raw_orcid":"https://orcid.org/0000-0001-5692-0832","affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL, USA","institution_ids":["https://openalex.org/I1282105669"]},{"raw_affiliation_string":"Northwestern University","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081856145","display_name":"Jorge Nocedal","orcid":"https://orcid.org/0000-0002-9662-2730"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jorge Nocedal","raw_affiliation_strings":["Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, USA","Northwestern University"],"raw_orcid":"https://orcid.org/0000-0002-9662-2730","affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, USA","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"Northwestern University","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5081856145"],"corresponding_institution_ids":["https://openalex.org/I111979921"],"apc_list":null,"apc_paid":null,"fwci":3.4212,"has_fulltext":true,"cited_by_count":33,"citation_normalized_percentile":{"value":0.9296994,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"35","issue":"4","first_page":"661","last_page":"680"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9998000264167786,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.799045205116272},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.5954631567001343},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5918034315109253},{"id":"https://openalex.org/keywords/newtons-method-in-optimization","display_name":"Newton's method in optimization","score":0.5831486582756042},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5100722908973694},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5027122497558594},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.479495108127594},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.4603353440761566},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4552035629749298},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.446866899728775},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.445705771446228},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4446309506893158},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4419027864933014},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.44028687477111816},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40243569016456604},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.24399074912071228},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.13656091690063477},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1143118143081665}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.799045205116272},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.5954631567001343},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5918034315109253},{"id":"https://openalex.org/C179127668","wikidata":"https://www.wikidata.org/wiki/Q17086396","display_name":"Newton's method in optimization","level":4,"score":0.5831486582756042},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5100722908973694},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5027122497558594},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.479495108127594},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.4603353440761566},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4552035629749298},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.446866899728775},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.445705771446228},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4446309506893158},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4419027864933014},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.44028687477111816},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40243569016456604},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.24399074912071228},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.13656091690063477},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1143118143081665},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1080/10556788.2020.1725751","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2020.1725751","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1705.06211","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1705.06211","pdf_url":"https://arxiv.org/pdf/1705.06211","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":"","raw_type":null},{"id":"pmh:oai:figshare.com:article/11987943","is_oa":true,"landing_page_url":null,"pdf_url":"https://figshare.com/articles/An_investigation_of_Newton-Sketch_and_subsampled_Newton_methods/11987943","source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:osti.gov:1657509","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1657509","pdf_url":"https://www.osti.gov/servlets/purl/1657509","source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null},{"id":"mag:2615262195","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1705.06211.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":"doi:10.48550/arxiv.1705.06211","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1705.06211","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"},{"id":"doi:10.6084/m9.figshare.11987943","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.11987943","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.6084/m9.figshare.11987943.v1","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.11987943.v1","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1705.06211","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1705.06211","pdf_url":"https://arxiv.org/pdf/1705.06211","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":"","raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1980957423","display_name":null,"funder_award_id":"N00014-14-1-0313","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G3314459484","display_name":"Collaborative Research:   Algorithms for Large-Scale Stochastic and Nonlinear Optimization","funder_award_id":"1620022","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4772581387","display_name":null,"funder_award_id":"DMS-1620022","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5449825205","display_name":null,"funder_award_id":"DMS-1620022","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"},{"id":"https://openalex.org/G5834367162","display_name":null,"funder_award_id":"N00014-14-1-0313 P00003","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320332815","display_name":"Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320335353","display_name":"National Science Foundation of Sri Lanka","ror":"https://ror.org/010xaa060"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W34239198","https://openalex.org/W1569098853","https://openalex.org/W1991083751","https://openalex.org/W1994616650","https://openalex.org/W2000769684","https://openalex.org/W2007399394","https://openalex.org/W2107438106","https://openalex.org/W2128237021","https://openalex.org/W2153635508","https://openalex.org/W2157988812","https://openalex.org/W2209036162","https://openalex.org/W2266946488","https://openalex.org/W2293249015","https://openalex.org/W2295465721","https://openalex.org/W2467074172","https://openalex.org/W2590556189","https://openalex.org/W2594182398","https://openalex.org/W2747280560","https://openalex.org/W2751113853","https://openalex.org/W2773306503","https://openalex.org/W2788452510","https://openalex.org/W2798909945","https://openalex.org/W2900789157","https://openalex.org/W2950523221","https://openalex.org/W2952215077","https://openalex.org/W2962961534","https://openalex.org/W2963060476","https://openalex.org/W2963262327","https://openalex.org/W2963307318","https://openalex.org/W2963397933","https://openalex.org/W2963433607","https://openalex.org/W2963483271","https://openalex.org/W2964063026","https://openalex.org/W2964216446","https://openalex.org/W3005768517","https://openalex.org/W3112410551","https://openalex.org/W3141595720","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W1991083751","https://openalex.org/W2107438106","https://openalex.org/W3029645440","https://openalex.org/W2963433607","https://openalex.org/W2900789157","https://openalex.org/W2524032428","https://openalex.org/W2293249015","https://openalex.org/W2146502635","https://openalex.org/W2061570747","https://openalex.org/W196761320","https://openalex.org/W2747280560","https://openalex.org/W2467074172","https://openalex.org/W2295465721","https://openalex.org/W2051434435","https://openalex.org/W3103657382","https://openalex.org/W2963060476","https://openalex.org/W1994616650","https://openalex.org/W1491622225","https://openalex.org/W6908809","https://openalex.org/W1569098853"],"abstract_inverted_index":{"Sketching,":[0],"a":[1,115,122,128],"dimensionality":[2,50],"reduction":[3,51],"technique,":[4],"has":[5,62],"received":[6],"much":[7],"attention":[8],"in":[9,19,30,52,74,88],"the":[10,20,32,75,85,90,110,132],"statistics":[11],"community.":[12],"In":[13],"this":[14],"paper,":[15],"we":[16],"study":[17,43,79],"sketching":[18,47],"context":[21],"of":[22,34,46,84,94,108,124,131],"Newton's":[23],"method":[24,113,135],"for":[25],"solving":[26],"finite-sum":[27],"optimization":[28,76],"problems":[29],"which":[31,89],"number":[33],"variables":[35],"and":[36,57,66,127],"data":[37,53],"points":[38],"are":[39,96,119],"both":[40],"large.":[41],"We":[42],"two":[44,86],"forms":[45],"that":[48],"perform":[49],"space:":[54],"Hessian":[55,133],"subsampling":[56,134],"randomized":[58],"Hadamard":[59],"transformations.":[60],"Each":[61],"its":[63],"own":[64],"advantages,":[65],"their":[67],"relative":[68],"tradeoffs":[69],"have":[70],"not":[71],"been":[72],"investigated":[73],"literature.":[77],"Our":[78],"focuses":[80],"on":[81],"practical":[82],"versions":[83],"methods":[87],"resulting":[91],"linear":[92],"systems":[93],"equations":[95],"solved":[97],"approximately,":[98],"at":[99],"every":[100],"iteration,":[101],"using":[102,109],"an":[103],"iterative":[104],"solver.":[105],"The":[106],"advantages":[107],"conjugate":[111],"gradient":[112,117],"vs.":[114],"stochastic":[116],"iteration":[118],"revealed":[120],"through":[121],"set":[123],"numerical":[125],"experiments,":[126],"complexity":[129],"analysis":[130],"is":[136],"presented.":[137]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2}],"updated_date":"2026-06-21T07:57:09.225873","created_date":"2025-10-10T00:00:00"}