{"id":"https://openalex.org/W2091352038","doi":"https://doi.org/10.1137/s0895479899359631","title":"Low-Rank Approximations with Sparse Factors I: Basic Algorithms and Error Analysis","display_name":"Low-Rank Approximations with Sparse Factors I: Basic Algorithms and Error Analysis","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2091352038","doi":"https://doi.org/10.1137/s0895479899359631","mag":"2091352038"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479899359631","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479899359631","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://escholarship.org/content/qt8816t6n9/qt8816t6n9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041743742","display_name":"Zhenyue Zhang","orcid":"https://orcid.org/0000-0002-2485-7004"},"institutions":[{"id":"https://openalex.org/I1284762954","display_name":"Zhejiang A & F University","ror":"https://ror.org/02vj4rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I1284762954"]},{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]},{"id":"https://openalex.org/I4179309","display_name":"Park University","ror":"https://ror.org/04ngpga37","country_code":"US","type":"education","lineage":["https://openalex.org/I4179309"]},{"id":"https://openalex.org/I4210151627","display_name":"National Energy Research Scientific Computing Center","ror":"https://ror.org/05v3mvq14","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521","https://openalex.org/I4210151627"]}],"countries":["CN","US"],"is_corresponding":true,"raw_author_name":"Zhenyue Zhang","raw_affiliation_strings":["National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory, One Cyclotron Road, M/S: SOF, Berkeley, CA 94720, USA","Center for Mathematical Sciences & Department of Applied Mathematics, Zhejiang Univer-sity, Hangzhou, 310027, P. R. China","Univer-sity Park, PA 16802, zhaiDcse.psu"],"affiliations":[{"raw_affiliation_string":"National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory, One Cyclotron Road, M/S: SOF, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I148283060","https://openalex.org/I4210151627"]},{"raw_affiliation_string":"Center for Mathematical Sciences & Department of Applied Mathematics, Zhejiang Univer-sity, Hangzhou, 310027, P. R. China","institution_ids":["https://openalex.org/I1284762954"]},{"raw_affiliation_string":"Univer-sity Park, PA 16802, zhaiDcse.psu","institution_ids":["https://openalex.org/I4179309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046703129","display_name":"Hongyuan Zha","orcid":"https://orcid.org/0000-0001-7493-0911"},"institutions":[{"id":"https://openalex.org/I1284762954","display_name":"Zhejiang A & F University","ror":"https://ror.org/02vj4rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I1284762954"]},{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]},{"id":"https://openalex.org/I4179309","display_name":"Park University","ror":"https://ror.org/04ngpga37","country_code":"US","type":"education","lineage":["https://openalex.org/I4179309"]},{"id":"https://openalex.org/I4210151627","display_name":"National Energy Research Scientific Computing Center","ror":"https://ror.org/05v3mvq14","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521","https://openalex.org/I4210151627"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Hongyuan Zha","raw_affiliation_strings":["Center for Mathematical Sciences & Department of Applied Mathematics, Zhejiang Univer-sity, Hangzhou, 310027, P. R. China","National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory, One Cyclotron Road, M/S: SOF, Berkeley, CA 94720, USA","Univer-sity Park, PA 16802, zhaiDcse.psu"],"affiliations":[{"raw_affiliation_string":"Center for Mathematical Sciences & Department of Applied Mathematics, Zhejiang Univer-sity, Hangzhou, 310027, P. R. China","institution_ids":["https://openalex.org/I1284762954"]},{"raw_affiliation_string":"National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory, One Cyclotron Road, M/S: SOF, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I148283060","https://openalex.org/I4210151627"]},{"raw_affiliation_string":"Univer-sity Park, PA 16802, zhaiDcse.psu","institution_ids":["https://openalex.org/I4179309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066426676","display_name":"Horst D. Simon","orcid":"https://orcid.org/0000-0003-0832-3720"},"institutions":[{"id":"https://openalex.org/I1284762954","display_name":"Zhejiang A & F University","ror":"https://ror.org/02vj4rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I1284762954"]},{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]},{"id":"https://openalex.org/I4179309","display_name":"Park University","ror":"https://ror.org/04ngpga37","country_code":"US","type":"education","lineage":["https://openalex.org/I4179309"]},{"id":"https://openalex.org/I4210151627","display_name":"National Energy Research Scientific Computing Center","ror":"https://ror.org/05v3mvq14","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521","https://openalex.org/I4210151627"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Horst Simon","raw_affiliation_strings":["Univer-sity Park, PA 16802, zhaiDcse.psu","National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory, One Cyclotron Road, M/S: SOF, Berkeley, CA 94720, USA","Center for Mathematical Sciences & Department of Applied Mathematics, Zhejiang Univer-sity, Hangzhou, 310027, P. R. China"],"affiliations":[{"raw_affiliation_string":"Univer-sity Park, PA 16802, zhaiDcse.psu","institution_ids":["https://openalex.org/I4179309"]},{"raw_affiliation_string":"National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory, One Cyclotron Road, M/S: SOF, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I148283060","https://openalex.org/I4210151627"]},{"raw_affiliation_string":"Center for Mathematical Sciences & Department of Applied Mathematics, Zhejiang Univer-sity, Hangzhou, 310027, P. R. China","institution_ids":["https://openalex.org/I1284762954"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5041743742"],"corresponding_institution_ids":["https://openalex.org/I1284762954","https://openalex.org/I148283060","https://openalex.org/I4179309","https://openalex.org/I4210151627"],"apc_list":null,"apc_paid":null,"fwci":5.1127,"has_fulltext":true,"cited_by_count":77,"citation_normalized_percentile":{"value":0.95596639,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"23","issue":"3","first_page":"706","last_page":"727"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9959999918937683,"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":0.9873999953269958,"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/rank","display_name":"Rank (graph theory)","score":0.7571008801460266},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.7395508289337158},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6748533248901367},{"id":"https://openalex.org/keywords/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.640410304069519},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6164716482162476},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.5335795283317566},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4707401692867279},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.4687376618385315},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.4654883146286011},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.45539066195487976},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.42161253094673157},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1327214241027832},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.11726406216621399},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08776381611824036}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7571008801460266},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.7395508289337158},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6748533248901367},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.640410304069519},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6164716482162476},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.5335795283317566},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4707401692867279},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.4687376618385315},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.4654883146286011},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.45539066195487976},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.42161253094673157},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1327214241027832},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.11726406216621399},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08776381611824036},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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/s0895479899359631","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479899359631","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:escholarship.org/ark:/13030/qt8816t6n9","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/8816t6n9","pdf_url":"https://escholarship.org/content/qt8816t6n9/qt8816t6n9.pdf","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal of Matrix Analysis, vol 23, iss 3","raw_type":"article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.8.8039","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.8.8039","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/slrap1.ps","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:escholarship.org/ark:/13030/qt8816t6n9","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/8816t6n9","pdf_url":"https://escholarship.org/content/qt8816t6n9/qt8816t6n9.pdf","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal of Matrix Analysis, vol 23, iss 3","raw_type":"article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1348557892","display_name":null,"funder_award_id":"DE-AC03-76SF00098","funder_id":"https://openalex.org/F4320337506","funder_display_name":"Advanced Scientific Computing Research"},{"id":"https://openalex.org/G1643223109","display_name":null,"funder_award_id":"AC03-76SF00098","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3451091241","display_name":null,"funder_award_id":"DE-AC03-76SF00098","funder_id":"https://openalex.org/F4320338292","funder_display_name":"Lawrence Berkeley National Laboratory"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G426315213","display_name":"Numerical Methods for large Eigenvalue Problems:            Parallizable Fast Algorithms and Inner-Outer iterations","funder_award_id":"9619452","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4323016164","display_name":null,"funder_award_id":"DE-AC03-76SF00098","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G5188851584","display_name":null,"funder_award_id":"71073","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"},{"id":"https://openalex.org/G5659161414","display_name":"Large-Scale Matrix Computation Problems in Information Retrieval and Datamining","funder_award_id":"9901986","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5921281487","display_name":null,"funder_award_id":"number","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6258415954","display_name":null,"funder_award_id":"Chinese","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6586271056","display_name":null,"funder_award_id":"DE-AC03-76SF00098","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"},{"id":"https://openalex.org/G6636457713","display_name":null,"funder_award_id":"6SF00098","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7245193638","display_name":null,"funder_award_id":"DE-AC03","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7500662759","display_name":null,"funder_award_id":"DE-AC03-76SF00","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8099852790","display_name":null,"funder_award_id":"DE-AC03-76SF00098","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8362473297","display_name":null,"funder_award_id":"71073","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8414908677","display_name":null,"funder_award_id":"DE-AC0","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"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"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320310419","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320334945","display_name":"Fok Ying Tong Education Foundation","ror":"https://ror.org/01mv9t934"},{"id":"https://openalex.org/F4320337506","display_name":"Advanced Scientific Computing Research","ror":"https://ror.org/0012c7r22"},{"id":"https://openalex.org/F4320338292","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02"},{"id":"https://openalex.org/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2091352038.pdf"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W83404773","https://openalex.org/W191724716","https://openalex.org/W1902027874","https://openalex.org/W1986583171","https://openalex.org/W2017895259","https://openalex.org/W2028781966","https://openalex.org/W2035445151","https://openalex.org/W2072773380","https://openalex.org/W2080051508","https://openalex.org/W2081331317","https://openalex.org/W2132582398","https://openalex.org/W2150126448"],"related_works":["https://openalex.org/W2154357715","https://openalex.org/W2952699400","https://openalex.org/W1925032196","https://openalex.org/W2336075021","https://openalex.org/W2951931073","https://openalex.org/W4304756082","https://openalex.org/W4298234822","https://openalex.org/W2782047334","https://openalex.org/W1970576574","https://openalex.org/W4094001"],"abstract_inverted_index":{"We":[0,53,77],"consider":[1],"the":[2,20,34,39,65,88],"problem":[3],"of":[4,8,13,36,38,59,92],"computing":[5],"low-rank":[6,21,68],"approximations":[7,22,69],"matrices.":[9],"The":[10],"novel":[11],"aspects":[12],"our":[14,60,93],"approach":[15],"are":[16],"that":[17],"we":[18],"require":[19],"to":[23,86],"be":[24,42],"written":[25],"in":[26],"a":[27,55],"factorized":[28],"form":[29],"with":[30,70],"sparse":[31,67],"factors,":[32],"and":[33,63,90],"degree":[35],"sparsity":[37],"factors":[40],"can":[41],"traded":[43],"off":[44],"for":[45],"reduced":[46],"reconstruction":[47],"error":[48,57],"by":[49],"certain":[50],"user-determined":[51],"parameters.":[52],"give":[54],"detailed":[56],"analysis":[58],"proposed":[61],"algorithms":[62],"compare":[64],"computed":[66],"those":[71],"obtained":[72],"from":[73,82],"singular":[74],"value":[75],"decomposition.":[76],"present":[78],"numerical":[79],"examples":[80],"arising":[81],"some":[83],"application":[84],"areas":[85],"illustrate":[87],"efficiency":[89],"accuracy":[91],"algorithms.":[94]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-14T08:04:32.555800","created_date":"2025-10-10T00:00:00"}
