{"id":"https://openalex.org/W2062037984","doi":"https://doi.org/10.1137/s1064827596308974","title":"Pivoted Cauchy-Like Preconditioners for Regularized Solution of Ill-Posed Problems","display_name":"Pivoted Cauchy-Like Preconditioners for Regularized Solution of Ill-Posed Problems","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2062037984","doi":"https://doi.org/10.1137/s1064827596308974","mag":"2062037984"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827596308974","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827596308974","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/A5041916316","display_name":"Misha E. Kilmer","orcid":"https://orcid.org/0000-0003-4249-4742"},"institutions":[{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]},{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Misha E. Kilmer","raw_affiliation_strings":["Applied Mathematics Program, University of Maryland, College Park, MD 20742"],"affiliations":[{"raw_affiliation_string":"Applied Mathematics Program, University of Maryland, College Park, MD 20742","institution_ids":["https://openalex.org/I66946132","https://openalex.org/I4210131439"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062480442","display_name":"Dianne P. O\u2019Leary","orcid":"https://orcid.org/0000-0001-9809-5180"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dianne P. O'Leary","raw_affiliation_strings":["Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062480442"],"corresponding_institution_ids":["https://openalex.org/I66946132"],"apc_list":null,"apc_paid":null,"fwci":3.0963,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.9096255,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":"1","first_page":"88","last_page":"110"},"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9979000091552734,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.8578605651855469},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8428279161453247},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.710393488407135},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.6265138983726501},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5941175818443298},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.534709095954895},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.530283510684967},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5228664875030518},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4771708548069},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.4160710275173187},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3511250615119934},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.33510199189186096},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.3030286133289337},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2872202396392822},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14838454127311707}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8578605651855469},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8428279161453247},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.710393488407135},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.6265138983726501},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5941175818443298},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.534709095954895},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.530283510684967},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5228664875030518},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4771708548069},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.4160710275173187},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3511250615119934},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.33510199189186096},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3030286133289337},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2872202396392822},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14838454127311707},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s1064827596308974","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827596308974","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.148.2839","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.148.2839","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.umd.edu/users/oleary/reprints/j50.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.24.4003","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.4003","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.umd.edu/Library/TRs/CS-TR-3682/CS-TR-3682.ps.Z","raw_type":"text"},{"id":"pmh:oai:drum.lib.umd.edu:1903/843","is_oa":false,"landing_page_url":"http://hdl.handle.net/1903/843","pdf_url":null,"source":{"id":"https://openalex.org/S4306402644","display_name":"Digital Repository at the University of Maryland (University of Maryland College Park)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66946132","host_organization_name":"University of Maryland, College Park","host_organization_lineage":["https://openalex.org/I66946132"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Technical Report"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W83404773","https://openalex.org/W114314968","https://openalex.org/W658559791","https://openalex.org/W1488435683","https://openalex.org/W1507705802","https://openalex.org/W1533471646","https://openalex.org/W1662925675","https://openalex.org/W1968735445","https://openalex.org/W1978157780","https://openalex.org/W1986721151","https://openalex.org/W1996557319","https://openalex.org/W2005140191","https://openalex.org/W2010961009","https://openalex.org/W2015071882","https://openalex.org/W2020163792","https://openalex.org/W2033093196","https://openalex.org/W2036932727","https://openalex.org/W2050001231","https://openalex.org/W2061813658","https://openalex.org/W2065578933","https://openalex.org/W2066687638","https://openalex.org/W2080097309","https://openalex.org/W2082779891","https://openalex.org/W2086260534","https://openalex.org/W2087111693","https://openalex.org/W2088955745","https://openalex.org/W2095508103","https://openalex.org/W2100420930","https://openalex.org/W2115066670","https://openalex.org/W2117366131","https://openalex.org/W2166298394","https://openalex.org/W2261382093","https://openalex.org/W2316564661","https://openalex.org/W4243081751"],"related_works":["https://openalex.org/W2349424752","https://openalex.org/W3046775784","https://openalex.org/W2382988560","https://openalex.org/W2024149451","https://openalex.org/W3031624508","https://openalex.org/W2977980606","https://openalex.org/W2525981419","https://openalex.org/W2033698563","https://openalex.org/W4322732133","https://openalex.org/W2956259592"],"abstract_inverted_index":{"Many":[0],"ill-posed":[1,126],"problems":[2,28],"are":[3,144,165],"solved":[4],"using":[5],"a":[6,11,16,20,71,79,92,102,180],"discretization":[7],"that":[8,60,120],"results":[9],"in":[10,46,66,108],"least":[12],"squares":[13],"problem":[14,38,127,181],"or":[15],"linear":[17],"system":[18],"involving":[19],"Toeplitz":[21,89],"matrix.":[22],"The":[23,168,185],"exact":[24],"solution":[25,52,59],"to":[26,76,91,100,153],"such":[27,78],"is":[29,39,128,193],"often":[30],"hopelessly":[31],"contaminated":[32],"by":[33],"noise,":[34],"since":[35],"the":[36,47,51,88,109,122,125,136,141,148,154,160,188],"discretized":[37],"quite":[40],"ill":[41],"conditioned,":[42],"and":[43,95,159,162],"noise":[44,192],"components":[45,65],"approximate":[48,58],"null-space":[49],"dominate":[50],"vector.":[53],"Therefore":[54],"we":[55,96],"seek":[56],"an":[57],"does":[61],"not":[62],"have":[63],"large":[64],"these":[67],"directions.":[68],"We":[69,118],"use":[70],"preconditioned":[72,142,169],"conjugate":[73],"gradient":[74],"algorithm":[75,170],"compute":[77],"regularized":[80],"solution.":[81],"A":[82],"unitary":[83],"change":[84],"of":[85,111,124,140,187],"coordinates":[86],"transforms":[87],"matrix":[90,106,143],"Cauchy-like":[93,105],"matrix,":[94],"choose":[97],"our":[98],"preconditioner":[99,132,189],"be":[101],"low":[103],"rank":[104],"determined":[107],"course":[110],"Gu's":[112],"fast":[113],"modified":[114],"complete":[115],"pivoting":[116],"algorithm.":[117],"show":[119],"if":[121],"kernel":[123],"smooth,":[129],"then":[130],"this":[131],"has":[133],"desirable":[134],"properties:":[135],"largest":[137],"singular":[138,150],"values":[139],"clustered":[145],"around":[146],"one,":[147],"smallest":[149],"values,":[151],"corresponding":[152],"lower":[155,163],"subspace,":[156],"remain":[157],"small,":[158],"upper":[161],"spaces":[164],"relatively":[166],"unmixed.":[167],"costs":[171],"only":[172],"O(n":[173],"lg":[174],"n)":[175],"operations":[176],"per":[177],"iteration":[178],"for":[179,190],"with":[182],"n":[183],"variables.":[184],"effectiveness":[186],"filtering":[191],"demonstrated":[194],"on":[195],"three":[196],"examples.":[197]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}