{"id":"https://openalex.org/W3103278656","doi":"https://doi.org/10.1137/20m1379617","title":"Subspace Recycling--Based Regularization Methods","display_name":"Subspace Recycling--Based Regularization Methods","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3103278656","doi":"https://doi.org/10.1137/20m1379617","mag":"3103278656"},"language":"en","primary_location":{"id":"doi:10.1137/20m1379617","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1379617","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/2011.05473","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083407680","display_name":"Ronny Ramlau","orcid":"https://orcid.org/0000-0002-0277-9615"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ronny Ramlau","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071268820","display_name":"Kirk M. Soodhalter","orcid":"https://orcid.org/0000-0003-0612-1199"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kirk M. Soodhalter","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5107223389","display_name":"Victoria Hutterer","orcid":"https://orcid.org/0000-0002-8952-2731"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Victoria Hutterer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08350343,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"42","issue":"4","first_page":"1480","last_page":"1505"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9987000226974487,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9861000180244446,"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/subspace-topology","display_name":"Subspace topology","score":0.817694365978241},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.626582145690918},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.5852157473564148},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5771728157997131},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5299072265625},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5294948220252991},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5185199975967407},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.48867538571357727},{"id":"https://openalex.org/keywords/well-posed-problem","display_name":"Well-posed problem","score":0.4717346429824829},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.45918625593185425},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44400957226753235},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.42410823702812195},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34836864471435547},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.284106582403183},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17112919688224792}],"concepts":[{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.817694365978241},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.626582145690918},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.5852157473564148},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5771728157997131},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5299072265625},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5294948220252991},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5185199975967407},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.48867538571357727},{"id":"https://openalex.org/C106214006","wikidata":"https://www.wikidata.org/wiki/Q1455898","display_name":"Well-posed problem","level":2,"score":0.4717346429824829},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.45918625593185425},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44400957226753235},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.42410823702812195},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34836864471435547},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.284106582403183},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17112919688224792},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1379617","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1379617","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2011.05473","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.05473","pdf_url":"https://arxiv.org/pdf/2011.05473","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":"text"},{"id":"mag:3103278656","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/2011.05473.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.2011.05473","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2011.05473","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2011.05473","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.05473","pdf_url":"https://arxiv.org/pdf/2011.05473","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":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7338003183","display_name":null,"funder_award_id":"F68-N36","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3103278656.pdf","grobid_xml":"https://content.openalex.org/works/W3103278656.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1544177383","https://openalex.org/W1545334034","https://openalex.org/W1570089119","https://openalex.org/W1975714268","https://openalex.org/W1982477720","https://openalex.org/W1987710178","https://openalex.org/W1990033625","https://openalex.org/W1994398423","https://openalex.org/W1994488194","https://openalex.org/W1998366068","https://openalex.org/W2001410384","https://openalex.org/W2005836623","https://openalex.org/W2015000924","https://openalex.org/W2042846224","https://openalex.org/W2043098752","https://openalex.org/W2046365642","https://openalex.org/W2052579356","https://openalex.org/W2059352204","https://openalex.org/W2073751862","https://openalex.org/W2094991849","https://openalex.org/W2122830560","https://openalex.org/W2340881874","https://openalex.org/W2407273549","https://openalex.org/W2782005976","https://openalex.org/W2894310252","https://openalex.org/W2953159856","https://openalex.org/W2964137678","https://openalex.org/W3010734322","https://openalex.org/W3039845887","https://openalex.org/W3098036980","https://openalex.org/W3098354209"],"related_works":["https://openalex.org/W2088886469","https://openalex.org/W1533460205","https://openalex.org/W3199991622","https://openalex.org/W2510600620","https://openalex.org/W3177915649","https://openalex.org/W2274178035","https://openalex.org/W2463534376","https://openalex.org/W3104509149","https://openalex.org/W2085045239","https://openalex.org/W1506063470","https://openalex.org/W2181753213","https://openalex.org/W1502711715","https://openalex.org/W3134155979","https://openalex.org/W3106359998","https://openalex.org/W3118064383","https://openalex.org/W2957344624","https://openalex.org/W3105299938","https://openalex.org/W2045266801","https://openalex.org/W2676810451","https://openalex.org/W1886579186"],"abstract_inverted_index":{"Subspace":[0],"recycling":[1,145],"techniques":[2],"have":[3,86,97],"been":[4,87],"used":[5],"quite":[6],"successfully":[7],"for":[8,14,43,89,103,196],"the":[9,45,50,58,64,90,104,148,157,172,192,197],"acceleration":[10],"of":[11,38,52,57,92,106,151,171,199],"iterative":[12,66,116],"methods":[13,20,85],"solving":[15,44],"large-scale":[16],"linear":[17,60,120],"systems.":[18],"These":[19],"often":[21],"work":[22],"by":[23,30,203],"augmenting":[24],"a":[25,31,35,54,77,124,131,144,152,162],"solution":[26,91,105],"subspace":[27,37,114,169],"generated":[28],"iteratively":[29],"known":[32,65],"algorithm":[33],"with":[34],"fixed":[36],"vectors":[39],"which":[40,63],"are":[41],"``useful''":[42],"problem.":[46],"Often,":[47],"this":[48,72,110],"has":[49],"effect":[51],"inducing":[53],"projected":[55],"version":[56,170],"original":[59],"system":[61],"to":[62,100,119],"method":[67,146,175],"is":[68,160],"then":[69,165],"applied,":[70],"and":[71,176,187],"projection":[73],"can":[74],"act":[75],"as":[76,154,156],"deflation":[78],"preconditioner,":[79],"accelerating":[80],"convergence.":[81],"Most":[82],"often,":[83],"these":[84,136],"applied":[88,118],"well-posed":[93],"problems.":[94,108],"However,":[95],"they":[96],"also":[98],"begun":[99],"be":[101],"considered":[102],"ill-posed":[107,121],"In":[109],"paper,":[111],"we":[112],"consider":[113],"augmentation-type":[115],"schemes":[117],"problems":[122,189],"in":[123],"continuous":[125],"Hilbert":[126],"space":[127],"setting,":[128],"based":[129],"on":[130,181,188],"recently":[132],"developed":[133],"framework":[134],"describing":[135],"methods.":[137],"We":[138,164],"show":[139],"that":[140],"under":[141],"suitable":[142],"assumptions,":[143],"satisfies":[147],"formal":[149],"definition":[150],"regularization,":[153],"long":[155],"underlying":[158],"scheme":[159],"itself":[161],"regularization.":[163],"develop":[166],"an":[167,182],"augmented":[168],"gradient":[173],"descent":[174],"demonstrate":[177],"its":[178],"effectiveness,":[179],"both":[180],"academic":[183],"Gaussian":[184],"blur":[185],"model":[186],"arising":[190],"from":[191],"adaptive":[193],"optics":[194],"community":[195],"resolution":[198],"large":[200,206],"sky":[201],"images":[202],"ground-based":[204],"extremely":[205],"telescopes.":[207]},"counts_by_year":[],"updated_date":"2026-07-01T08:55:40.977307","created_date":"2025-10-10T00:00:00"}