{"id":"https://openalex.org/W2765351577","doi":"https://doi.org/10.1515/cmam-2018-0030","title":"A Low-Rank Inexact Newton\u2013Krylov Method for Stochastic Eigenvalue Problems","display_name":"A Low-Rank Inexact Newton\u2013Krylov Method for Stochastic Eigenvalue Problems","publication_year":2018,"publication_date":"2018-07-21","ids":{"openalex":"https://openalex.org/W2765351577","doi":"https://doi.org/10.1515/cmam-2018-0030","mag":"2765351577"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2018-0030","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0030","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1710.09470","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Peter Benner","orcid":null},"institutions":[{"id":"https://openalex.org/I4210127568","display_name":"Max Planck Institute for Dynamics of Complex Technical Systems","ror":"https://ror.org/030h7k016","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210127568"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Peter Benner","raw_affiliation_strings":["Computational Methods in Systems and Control Theory , Max Planck Institute for Dynamics of Complex Technical Systems , Sandtorstr. 1, 39106 Magdeburg , Germany"],"affiliations":[{"raw_affiliation_string":"Computational Methods in Systems and Control Theory , Max Planck Institute for Dynamics of Complex Technical Systems , Sandtorstr. 1, 39106 Magdeburg , Germany","institution_ids":["https://openalex.org/I4210127568"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Akwum Onwunta","orcid":null},"institutions":[{"id":"https://openalex.org/I4210127568","display_name":"Max Planck Institute for Dynamics of Complex Technical Systems","ror":"https://ror.org/030h7k016","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210127568"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Akwum Onwunta","raw_affiliation_strings":["Computational Methods in Systems and Control Theory , Max Planck Institute for Dynamics of Complex Technical Systems , Sandtorstr. 1, 39106 Magdeburg , Germany"],"affiliations":[{"raw_affiliation_string":"Computational Methods in Systems and Control Theory , Max Planck Institute for Dynamics of Complex Technical Systems , Sandtorstr. 1, 39106 Magdeburg , Germany","institution_ids":["https://openalex.org/I4210127568"]}]},{"author_position":"last","author":{"id":null,"display_name":"Martin Stoll","orcid":null},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Stoll","raw_affiliation_strings":["Faculty of Mathematics , Professorship Scientific Computing , Technische Universit\u00e4t Chemnitz , 09107 Chemnitz , Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics , Professorship Scientific Computing , Technische Universit\u00e4t Chemnitz , 09107 Chemnitz , Germany","institution_ids":["https://openalex.org/I2610724"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210127568"],"apc_list":null,"apc_paid":null,"fwci":0.629,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.60576923,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"19","issue":"1","first_page":"5","last_page":"22"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.6425999999046326,"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"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.6425999999046326,"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"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.09040000289678574,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.06989999860525131,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6956999897956848},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.6561999917030334},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6550999879837036},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6466000080108643},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.46639999747276306},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.46480000019073486}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6956999897956848},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.6561999917030334},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6550999879837036},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6466000080108643},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5989000201225281},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5920000076293945},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.46639999747276306},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.46480000019073486},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4260999858379364},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4239000082015991},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3959999978542328},{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.2903999984264374},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28380000591278076},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.26019999384880066}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/cmam-2018-0030","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0030","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1710.09470","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.09470","pdf_url":"https://arxiv.org/pdf/1710.09470","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1710.09470","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.09470","pdf_url":"https://arxiv.org/pdf/1710.09470","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1538934584","https://openalex.org/W1889120202","https://openalex.org/W1961414889","https://openalex.org/W1963497044","https://openalex.org/W1972350501","https://openalex.org/W1973836629","https://openalex.org/W1985289051","https://openalex.org/W1994722534","https://openalex.org/W1995371856","https://openalex.org/W1997969642","https://openalex.org/W1998576042","https://openalex.org/W2018850201","https://openalex.org/W2024528718","https://openalex.org/W2030605445","https://openalex.org/W2040960244","https://openalex.org/W2048369486","https://openalex.org/W2073560717","https://openalex.org/W2079440004","https://openalex.org/W2088087394","https://openalex.org/W2102031020","https://openalex.org/W2107501462","https://openalex.org/W2115308285","https://openalex.org/W2119175729","https://openalex.org/W2120494006","https://openalex.org/W2126195988","https://openalex.org/W2130416410","https://openalex.org/W2133437030","https://openalex.org/W2134693763","https://openalex.org/W2135459060","https://openalex.org/W2136889760","https://openalex.org/W2140153041","https://openalex.org/W2141870784","https://openalex.org/W2143956837","https://openalex.org/W2155216327","https://openalex.org/W2255903624","https://openalex.org/W2268206128","https://openalex.org/W2323937450","https://openalex.org/W2480854438","https://openalex.org/W2962828807","https://openalex.org/W4231405723","https://openalex.org/W4300580367"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"aims":[3],"at":[4],"the":[5,28,52,57],"efficient":[6],"numerical":[7,63],"solution":[8],"of":[9,59],"stochastic":[10,29,53],"eigenvalue":[11],"problems.":[12],"Such":[13],"problems":[14],"often":[15],"lead":[16],"to":[17,40],"prohibitively":[18],"high-dimensional":[19],"systems":[20],"with":[21,27,48,62],"tensor":[22,37],"product":[23,38],"structure":[24,39],"when":[25],"discretized":[26],"Galerkin":[30],"method.":[31],"Here,":[32],"we":[33,50],"exploit":[34],"this":[35],"inherent":[36],"develop":[41],"a":[42],"globalized":[43],"low-rank":[44],"inexact":[45],"Newton":[46],"method":[47],"which":[49],"tackle":[51],"eigenproblem.":[54],"We":[55],"illustrate":[56],"effectiveness":[58],"our":[60],"solver":[61],"experiments.":[64]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2017-11-10T00:00:00"}