{"id":"https://openalex.org/W2017895259","doi":"https://doi.org/10.1137/s1064827597327309","title":"Low-Rank Matrix Approximation Using the Lanczos Bidiagonalization Process with Applications","display_name":"Low-Rank Matrix Approximation Using the Lanczos Bidiagonalization Process with Applications","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2017895259","doi":"https://doi.org/10.1137/s1064827597327309","mag":"2017895259"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827597327309","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827597327309","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/A5066426676","display_name":"Horst D. Simon","orcid":"https://orcid.org/0000-0003-0832-3720"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Horst D. Simon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5046703129","display_name":"Hongyuan Zha","orcid":"https://orcid.org/0000-0001-7493-0911"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hongyuan Zha","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":2.7185,"has_fulltext":false,"cited_by_count":146,"citation_normalized_percentile":{"value":0.88608899,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"21","issue":"6","first_page":"2257","last_page":"2274"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9894000291824341,"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":0.9894000291824341,"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":0.9873999953269958,"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"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9771999716758728,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/lanczos-resampling","display_name":"Lanczos resampling","score":0.8507696390151978},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.8479588031768799},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.7413622140884399},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6844034790992737},{"id":"https://openalex.org/keywords/lanczos-algorithm","display_name":"Lanczos algorithm","score":0.6463618874549866},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.6338548064231873},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.6059775948524475},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6008778810501099},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5681537389755249},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.5038887858390808},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4911288917064667},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44169488549232483},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41739484667778015},{"id":"https://openalex.org/keywords/hankel-matrix","display_name":"Hankel matrix","score":0.2083549201488495},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.19972151517868042},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1538909375667572},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14177781343460083}],"concepts":[{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.8507696390151978},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.8479588031768799},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.7413622140884399},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6844034790992737},{"id":"https://openalex.org/C20501136","wikidata":"https://www.wikidata.org/wiki/Q366640","display_name":"Lanczos algorithm","level":4,"score":0.6463618874549866},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.6338548064231873},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.6059775948524475},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6008778810501099},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5681537389755249},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.5038887858390808},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4911288917064667},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44169488549232483},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41739484667778015},{"id":"https://openalex.org/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.2083549201488495},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.19972151517868042},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1538909375667572},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14177781343460083},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s1064827597327309","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827597327309","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:10.1.1.17.1230","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.1230","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cse.psu.edu/~zha/papers/lowrank.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.295.1562","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.295.1562","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.stanford.edu/group/SOL/papers/SimonZha2000.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1776944688","https://openalex.org/W1809965678","https://openalex.org/W1918870341","https://openalex.org/W1996375718","https://openalex.org/W2005423095","https://openalex.org/W2006043357","https://openalex.org/W2008297189","https://openalex.org/W2020285660","https://openalex.org/W2022059930","https://openalex.org/W2035864055","https://openalex.org/W2059029453","https://openalex.org/W2059586807","https://openalex.org/W2073835183","https://openalex.org/W2097897435","https://openalex.org/W2138451337","https://openalex.org/W2158495995","https://openalex.org/W2798501834","https://openalex.org/W2798909945","https://openalex.org/W3046265042"],"related_works":["https://openalex.org/W749579920","https://openalex.org/W2024281837","https://openalex.org/W1965497533","https://openalex.org/W4301887332","https://openalex.org/W2017895259","https://openalex.org/W30499333","https://openalex.org/W2903666957","https://openalex.org/W2135569577","https://openalex.org/W1730730025","https://openalex.org/W2889042866"],"abstract_inverted_index":{"Low-rank":[0],"approximation":[1],"of":[2,72,89,100],"large":[3],"and/or":[4],"sparse":[5],"matrices":[6],"is":[7],"important":[8],"in":[9],"many":[10],"applications,":[11],"and":[12,78,98],"the":[13,19,42,48,75,86,90,96],"singular":[14],"value":[15],"decomposition":[16],"(SVD)":[17],"gives":[18],"best":[20],"low-rank":[21,35,81],"approximations":[22,36],"with":[23],"respect":[24],"to":[25,47,67],"unitarily-invariant":[26],"norms.":[27],"In":[28],"this":[29],"paper":[30],"we":[31],"show":[32],"that":[33,58],"good":[34],"can":[37,64],"be":[38,65],"directly":[39],"obtained":[40],"from":[41,106],"Lanczos":[43,76,91],"bidiagonalization":[44,92],"process":[45,63],"applied":[46],"given":[49],"matrix":[50],"without":[51],"computing":[52],"any":[53],"SVD.":[54],"We":[55,94],"also":[56],"demonstrate":[57],"a":[59],"so-called":[60],"one-sided":[61],"reorthogonalization":[62],"used":[66],"maintain":[68],"an":[69],"adequate":[70],"level":[71],"orthogonality":[73],"among":[74],"vectors":[77],"produce":[79],"accurate":[80],"approximations.":[82],"This":[83],"technique":[84],"reduces":[85],"computational":[87],"cost":[88],"process.":[93],"illustrate":[95],"efficiency":[97],"applicability":[99],"our":[101],"algorithm":[102],"using":[103],"numerical":[104],"examples":[105],"several":[107],"applications":[108],"areas.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
