{"id":"https://openalex.org/W2043448909","doi":"https://doi.org/10.1137/s106482750240649x","title":"A Robust Preconditioner with Low Memory Requirements for Large Sparse Least Squares Problems","display_name":"A Robust Preconditioner with Low Memory Requirements for Large Sparse Least Squares Problems","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2043448909","doi":"https://doi.org/10.1137/s106482750240649x","mag":"2043448909"},"language":"en","primary_location":{"id":"doi:10.1137/s106482750240649x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s106482750240649x","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/A5053109099","display_name":"Michele Benzi","orcid":"https://orcid.org/0000-0001-6099-0294"},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michele Benzi","raw_affiliation_strings":["Emory University"],"affiliations":[{"raw_affiliation_string":"Emory University","institution_ids":["https://openalex.org/I150468666"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053422141","display_name":"Miroslav T\u016fma","orcid":"https://orcid.org/0000-0003-2808-6929"},"institutions":[{"id":"https://openalex.org/I202391551","display_name":"Czech Academy of Sciences","ror":"https://ror.org/053avzc18","country_code":"CZ","type":"funder","lineage":["https://openalex.org/I202391551"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Miroslav Tuma","raw_affiliation_strings":["Czech Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Czech Academy of Sciences","institution_ids":["https://openalex.org/I202391551"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053109099"],"corresponding_institution_ids":["https://openalex.org/I150468666"],"apc_list":null,"apc_paid":null,"fwci":2.1807,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.8743866,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"25","issue":"2","first_page":"499","last_page":"512"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9969000220298767,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9937999844551086,"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":0.9590003490447998},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6493128538131714},{"id":"https://openalex.org/keywords/incomplete-lu-factorization","display_name":"Incomplete LU factorization","score":0.610511302947998},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5986692309379578},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.5459086894989014},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5298944115638733},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.5178947448730469},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.5117725729942322},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4958373010158539},{"id":"https://openalex.org/keywords/incomplete-cholesky-factorization","display_name":"Incomplete Cholesky factorization","score":0.4876502752304077},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.42186325788497925},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4198130965232849},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4156422019004822},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.2383025586605072},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.17770394682884216},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10604813694953918}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9590003490447998},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6493128538131714},{"id":"https://openalex.org/C134978465","wikidata":"https://www.wikidata.org/wiki/Q1654069","display_name":"Incomplete LU factorization","level":4,"score":0.610511302947998},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5986692309379578},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5459086894989014},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5298944115638733},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.5178947448730469},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5117725729942322},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4958373010158539},{"id":"https://openalex.org/C44363057","wikidata":"https://www.wikidata.org/wiki/Q6015160","display_name":"Incomplete Cholesky factorization","level":4,"score":0.4876502752304077},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.42186325788497925},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4198130965232849},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4156422019004822},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2383025586605072},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.17770394682884216},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10604813694953918},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"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/s106482750240649x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s106482750240649x","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:10.1.1.117.8516","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.8516","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathcs.emory.edu/~benzi/Web_papers/copper.pdf","raw_type":"text"},{"id":"pmh:oai:ricerca.sns.it:11384/75303","is_oa":false,"landing_page_url":"http://hdl.handle.net/11384/75303","pdf_url":null,"source":{"id":"https://openalex.org/S7407050981","display_name":"Scuola Normale Superiore di Pisa","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W10284890","https://openalex.org/W92381197","https://openalex.org/W219611153","https://openalex.org/W1488292267","https://openalex.org/W1555926138","https://openalex.org/W1971440257","https://openalex.org/W1977444623","https://openalex.org/W1986310461","https://openalex.org/W2003550247","https://openalex.org/W2010315317","https://openalex.org/W2025836747","https://openalex.org/W2027532376","https://openalex.org/W2032229464","https://openalex.org/W2044557804","https://openalex.org/W2051633585","https://openalex.org/W2058997431","https://openalex.org/W2063675347","https://openalex.org/W2067576119","https://openalex.org/W2070419067","https://openalex.org/W2078637543","https://openalex.org/W2097897435","https://openalex.org/W2473084598","https://openalex.org/W2508453802","https://openalex.org/W4205589782","https://openalex.org/W4243795446","https://openalex.org/W4245301022","https://openalex.org/W4285719527","https://openalex.org/W4302564868"],"related_works":["https://openalex.org/W2025836747","https://openalex.org/W2095258827","https://openalex.org/W2046537284","https://openalex.org/W2381435995","https://openalex.org/W2055020807","https://openalex.org/W1991619898","https://openalex.org/W2142399659","https://openalex.org/W2962801049","https://openalex.org/W4300829789","https://openalex.org/W2283569199"],"abstract_inverted_index":{"This":[0],"paper":[1],"describes":[2],"a":[3],"technique":[4],"for":[5,9],"constructing":[6],"robust":[7],"preconditioners":[8,74],"the":[10,15,32,37,41,62,65],"CGLS":[11],"method":[12],"applied":[13],"to":[14,39],"solution":[16],"of":[17,31,64],"large":[18],"and":[19,53],"sparse":[20],"least":[21],"squares":[22],"problems.":[23],"The":[24,45],"algorithm":[25],"computes":[26],"an":[27],"incomplete":[28,72],"LDLT":[29],"factorization":[30],"normal":[33,42],"equations":[34],"matrix":[35,43],"without":[36],"need":[38],"form":[40],"itself.":[44],"preconditioner":[46,66],"is":[47,75],"reliable":[48],"(pivot":[49],"breakdowns":[50],"cannot":[51],"occur)":[52],"has":[54],"low":[55],"intermediate":[56],"storage":[57],"requirements.":[58],"Numerical":[59],"experiments":[60],"illustrating":[61],"performance":[63],"are":[67],"presented.":[68],"A":[69],"comparison":[70],"with":[71],"QR":[73],"also":[76],"included.":[77]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}