{"id":"https://openalex.org/W2056346372","doi":"https://doi.org/10.1137/0915047","title":"Iterative SVD-Based Methods for Ill-Posed Problems","display_name":"Iterative SVD-Based Methods for Ill-Posed Problems","publication_year":1994,"publication_date":"1994-05-01","ids":{"openalex":"https://openalex.org/W2056346372","doi":"https://doi.org/10.1137/0915047","mag":"2056346372"},"language":"en","primary_location":{"id":"doi:10.1137/0915047","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0915047","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/A5111718578","display_name":"C. R. Vogel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. R. Vogel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5025936032","display_name":"J.G. Wade","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. G. Wade","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":2.8992,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.90381125,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"15","issue":"3","first_page":"736","last_page":"754"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"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":0.9998999834060669,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.8103867769241333},{"id":"https://openalex.org/keywords/lanczos-resampling","display_name":"Lanczos resampling","score":0.7345089316368103},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.7006410360336304},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6852385997772217},{"id":"https://openalex.org/keywords/well-posed-problem","display_name":"Well-posed problem","score":0.6167352199554443},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5875750184059143},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5827131867408752},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5239431858062744},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5181523561477661},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.5099951028823853},{"id":"https://openalex.org/keywords/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.48831960558891296},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4430680572986603},{"id":"https://openalex.org/keywords/numerical-linear-algebra","display_name":"Numerical linear algebra","score":0.43465346097946167},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4322138726711273},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4321633279323578},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42895346879959106},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4234652519226074},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4025845527648926},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25239068269729614},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21243715286254883},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.15881270170211792}],"concepts":[{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.8103867769241333},{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.7345089316368103},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.7006410360336304},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6852385997772217},{"id":"https://openalex.org/C106214006","wikidata":"https://www.wikidata.org/wiki/Q1455898","display_name":"Well-posed problem","level":2,"score":0.6167352199554443},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5875750184059143},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5827131867408752},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5239431858062744},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5181523561477661},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.5099951028823853},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.48831960558891296},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4430680572986603},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.43465346097946167},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4322138726711273},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4321633279323578},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42895346879959106},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4234652519226074},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4025845527648926},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25239068269729614},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21243715286254883},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.15881270170211792},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/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},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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":1,"locations":[{"id":"doi:10.1137/0915047","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0915047","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W114314968","https://openalex.org/W346091471","https://openalex.org/W1968735445","https://openalex.org/W1976798627","https://openalex.org/W1998430389","https://openalex.org/W2005836623","https://openalex.org/W2008298717","https://openalex.org/W2017387343","https://openalex.org/W2019462010","https://openalex.org/W2031604650","https://openalex.org/W2053412105","https://openalex.org/W2063819119","https://openalex.org/W2068484625","https://openalex.org/W2120665288","https://openalex.org/W2123944402","https://openalex.org/W2137645797","https://openalex.org/W2158495995","https://openalex.org/W3022793637","https://openalex.org/W3152500676","https://openalex.org/W4213170243","https://openalex.org/W4251656402","https://openalex.org/W4292232969"],"related_works":["https://openalex.org/W2950418232","https://openalex.org/W4301683480","https://openalex.org/W2889932903","https://openalex.org/W1987723384","https://openalex.org/W1964004266","https://openalex.org/W3201061354","https://openalex.org/W2512523917","https://openalex.org/W4242776319","https://openalex.org/W1977732568","https://openalex.org/W2801545606"],"abstract_inverted_index":{"Very":[0],"large":[1],"matrices":[2],"with":[3],"rapidly":[4],"decaying":[5],"singular":[6,18,52,57],"values":[7,53],"commonly":[8],"arise":[9],"in":[10,110],"the":[11,28,50,70,74,79,87,104,107],"numerical":[12,95],"solution":[13],"of":[14,32,48,83,89,97,106],"ill-posed":[15,90],"problems.":[16,36],"The":[17],"value":[19],"decomposition":[20],"(SVD)":[21],"is":[22,101,113],"a":[23,44],"basic":[24],"tool":[25],"for":[26,78],"both":[27],"analysis":[29],"and":[30,54,69,94,103],"computation":[31,82],"solutions":[33],"to":[34,42],"such":[35],"In":[37,59,86],"most":[38],"applications,":[39],"it":[40],"suffices":[41],"obtain":[43],"partial":[45,84],"SVD":[46],"consisting":[47],"only":[49],"largest":[51],"their":[55],"corresponding":[56],"vectors.":[58],"this":[60],"paper,":[61],"two":[62,99],"separate":[63],"approaches\u2014one":[64],"based":[65,72],"on":[66,73],"subspace":[67],"iteration":[68],"other":[71],"Lanczos":[75],"method\u2014are":[76],"considered":[77],"efficient":[80],"iterative":[81],"SVDs.":[85],"context":[88],"problems,":[91],"an":[92],"analytical":[93],"comparison":[96],"these":[98],"methods":[100],"made":[102],"role":[105],"regularization":[108],"operator":[109],"convergence":[111],"acceleration":[112],"explored.":[114]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}