{"id":"https://openalex.org/W2809843622","doi":"https://doi.org/10.1137/17m1121342","title":"Low-Rank Eigenvector Compression of Posterior Covariance Matrices for Linear Gaussian Inverse Problems","display_name":"Low-Rank Eigenvector Compression of Posterior Covariance Matrices for Linear Gaussian Inverse Problems","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2809843622","doi":"https://doi.org/10.1137/17m1121342","mag":"2809843622"},"language":"en","primary_location":{"id":"doi:10.1137/17m1121342","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1121342","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1703.05638","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060985095","display_name":"Peter Benner","orcid":"https://orcid.org/0000-0003-3362-4103"},"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 Group, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computational Methods in Systems and Control Theory Group, 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":"https://openalex.org/A5008509143","display_name":"Yue Qiu","orcid":"https://orcid.org/0000-0003-0360-0442"},"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"]},{"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":"Yue Qiu","raw_affiliation_strings":["Computational Methods in Systems and Control Theory Group, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany","), and Professorship of Scientific Computing, Faculty of Mathematics, Technische Universit\u00e4t Chemnitz, 09107 Chemnitz, Germany,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computational Methods in Systems and Control Theory Group, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany","institution_ids":["https://openalex.org/I4210127568"]},{"raw_affiliation_string":"), and Professorship of Scientific Computing, Faculty of Mathematics, Technische Universit\u00e4t Chemnitz, 09107 Chemnitz, Germany,","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055578402","display_name":"Martin Stoll","orcid":"https://orcid.org/0000-0003-0951-4756"},"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":"Martin Stoll","raw_affiliation_strings":["Numerical Linear Algebra for Dynamical Systems Group, Max Planck Institute for Dynamics of Complex Tech-nical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Numerical Linear Algebra for Dynamical Systems Group, Max Planck Institute for Dynamics of Complex Tech-nical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany","institution_ids":["https://openalex.org/I4210127568"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8327,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.70192882,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"6","issue":"2","first_page":"965","last_page":"989"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9988999962806702,"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":0.9988999962806702,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9980999827384949,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied 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/covariance","display_name":"Covariance","score":0.6749271154403687},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6297165155410767},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5409693121910095},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5173534750938416},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5152433514595032},{"id":"https://openalex.org/keywords/posterior-probability","display_name":"Posterior probability","score":0.5100730061531067},{"id":"https://openalex.org/keywords/estimation-of-covariance-matrices","display_name":"Estimation of covariance matrices","score":0.48948967456817627},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4835819602012634},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.47926995158195496},{"id":"https://openalex.org/keywords/covariance-function","display_name":"Covariance function","score":0.46789562702178955},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4452899694442749},{"id":"https://openalex.org/keywords/rational-quadratic-covariance-function","display_name":"Rational quadratic covariance function","score":0.43510299921035767},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.4308590888977051},{"id":"https://openalex.org/keywords/mat\u00e9rn-covariance-function","display_name":"Mat\u00e9rn covariance function","score":0.42243507504463196},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4126129150390625},{"id":"https://openalex.org/keywords/covariance-intersection","display_name":"Covariance intersection","score":0.29684072732925415},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22433826327323914},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.18931666016578674},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15181022882461548}],"concepts":[{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6749271154403687},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6297165155410767},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5409693121910095},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5173534750938416},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5152433514595032},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.5100730061531067},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.48948967456817627},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4835819602012634},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.47926995158195496},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.46789562702178955},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4452899694442749},{"id":"https://openalex.org/C148893098","wikidata":"https://www.wikidata.org/wiki/Q7295778","display_name":"Rational quadratic covariance function","level":5,"score":0.43510299921035767},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.4308590888977051},{"id":"https://openalex.org/C118006245","wikidata":"https://www.wikidata.org/wiki/Q6792079","display_name":"Mat\u00e9rn covariance function","level":5,"score":0.42243507504463196},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4126129150390625},{"id":"https://openalex.org/C83042196","wikidata":"https://www.wikidata.org/wiki/Q5178898","display_name":"Covariance intersection","level":4,"score":0.29684072732925415},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22433826327323914},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.18931666016578674},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15181022882461548},{"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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/17m1121342","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1121342","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1703.05638","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1703.05638","pdf_url":"https://arxiv.org/pdf/1703.05638","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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:escidoc.org:escidoc:2474802","is_oa":true,"landing_page_url":"http://hdl.handle.net/21.11116/0000-0000-2E2A-F","pdf_url":null,"source":{"id":"https://openalex.org/S7407052962","display_name":"Max Planck Digital Library","issn_l":null,"issn":[],"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":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1703.05638","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1703.05638","pdf_url":"https://arxiv.org/pdf/1703.05638","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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/G2430735070","display_name":null,"funder_award_id":"ZS/2016/04/78156","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"}],"funders":[{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320335828","display_name":"Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg","ror":"https://ror.org/030h7k016"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2809843622.pdf","grobid_xml":"https://content.openalex.org/works/W2809843622.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W50417968","https://openalex.org/W1563653928","https://openalex.org/W1579781026","https://openalex.org/W1600371943","https://openalex.org/W1963497044","https://openalex.org/W1964200011","https://openalex.org/W1967077133","https://openalex.org/W1968119930","https://openalex.org/W1986724944","https://openalex.org/W1996869553","https://openalex.org/W2022819055","https://openalex.org/W2026993378","https://openalex.org/W2050959344","https://openalex.org/W2059735442","https://openalex.org/W2074836377","https://openalex.org/W2075097820","https://openalex.org/W2088087394","https://openalex.org/W2113020599","https://openalex.org/W2117686912","https://openalex.org/W2126566496","https://openalex.org/W2139257007","https://openalex.org/W2149498546","https://openalex.org/W2169328438","https://openalex.org/W2462634212","https://openalex.org/W2480611454","https://openalex.org/W2962707560","https://openalex.org/W2963698472","https://openalex.org/W2963852881","https://openalex.org/W2963964397","https://openalex.org/W3101167228"],"related_works":["https://openalex.org/W2022823194","https://openalex.org/W2103482025","https://openalex.org/W4248223124","https://openalex.org/W2126916073","https://openalex.org/W3211883524","https://openalex.org/W2050407974","https://openalex.org/W1991005374","https://openalex.org/W3025277714","https://openalex.org/W4386993326","https://openalex.org/W1987404909"],"abstract_inverted_index":{"We":[0,121,189,207,222],"consider":[1],"the":[2,8,12,23,27,30,34,46,52,58,63,67,76,91,99,113,124,127,143,151,164,174,177,183,186,203,210,228],"problem":[3,41],"of":[4,7,11,26,36,57,66,78,126,169,176,185,230],"efficient":[5],"computations":[6],"covariance":[9,55,64,101],"matrix":[10,56,65,81,102],"posterior":[13,59,68,100],"probability":[14,24,60,69],"density":[15,25,70],"for":[16,84,93,110,153],"linear":[17],"Gaussian":[18],"Bayesian":[19],"inverse":[20,40],"problems.":[21],"When":[22],"noise":[28],"and":[29,54,73,136,142,166,180,213],"prior":[31],"are":[32],"Gaussian,":[33],"solution":[35,48],"such":[37,79,131],"a":[38,80,132,191,196],"statistical":[39],"is":[42,49,71,82,90,146,173,182],"also":[43],"Gaussian.":[44],"Therefore,":[45],"underlying":[47],"characterized":[50],"by":[51,163],"mean":[53],"density.":[61],"However,":[62],"dense":[72],"large.":[74],"Hence,":[75],"computation":[77,165],"impossible":[83],"large":[85],"dimensional":[86],"parameter":[87],"spaces":[88],"as":[89,106],"case":[92],"discretized":[94,128],"PDEs.":[95],"Low-rank":[96],"approximations":[97],"to":[98,159,218,226],"were":[103],"recently":[104],"introduced":[105],"promising":[107],"tools.":[108],"Nevertheless,":[109],"transient":[111],"problems":[112],"resulting":[114],"approximation":[115,157],"suffers":[116],"from":[117,216],"an":[118,154],"increased":[119],"dimensionality.":[120],"here":[122],"exploit":[123],"structure":[125],"equations":[129],"in":[130,198],"way":[133],"that":[134,194],"spatial":[135,178],"temporal":[137],"components":[138],"can":[139],"be":[140],"separated":[141],"growing":[144],"complexity":[145,168,212],"dramatically":[147],"reduced.":[148],"In":[149],"particular,":[150],"storage":[152,167,214],"eigenvector":[155],"low-rank":[156,197,204],"up":[158],"now":[160],"was":[161],"dominated":[162],"$\\mathcal{O}({n_x}{n_t})$,":[170],"where":[171],"${n_x}$":[172],"dimension":[175,184],"domain":[179],"${n_t}$":[181],"time":[187,199],"domain.":[188],"develop":[190],"new":[192],"approach":[193],"utilizes":[195],"algorithm":[200],"together":[201],"with":[202],"Hessian":[205],"method.":[206],"reduce":[208],"both":[209],"computational":[211],"requirement":[215],"$\\mathcal{O}({n_x}{n_t})$":[217],"$\\mathcal{O}({n_x}":[219],"+":[220],"{n_t})$.":[221],"use":[223],"numerical":[224],"experiments":[225],"illustrate":[227],"advantages":[229],"our":[231],"approach.":[232]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2018-07-10T00:00:00"}