{"id":"https://openalex.org/W2162572068","doi":"https://doi.org/10.1002/nla.1973","title":"Truncated low\u2010rank methods for solving general linear matrix equations","display_name":"Truncated low\u2010rank methods for solving general linear matrix equations","publication_year":2015,"publication_date":"2015-03-04","ids":{"openalex":"https://openalex.org/W2162572068","doi":"https://doi.org/10.1002/nla.1973","mag":"2162572068"},"language":"en","primary_location":{"id":"doi:10.1002/nla.1973","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.1973","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/208146","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084601962","display_name":"Daniel Kre\u00dfner","orcid":"https://orcid.org/0000-0003-3369-2958"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Daniel Kressner","raw_affiliation_strings":["Chair of Numerical Algorithms and HPC MATHICSE, EPF Lausanne  CH\u20101015 Lausanne Switzerland","Chair of Numerical Algorithms and HPC, MATHICSE, EPF Lausanne, CH-1015 Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Chair of Numerical Algorithms and HPC MATHICSE, EPF Lausanne  CH\u20101015 Lausanne Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Chair of Numerical Algorithms and HPC, MATHICSE, EPF Lausanne, CH-1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048101802","display_name":"Petar Sirkovi\u0107","orcid":"https://orcid.org/0000-0003-2779-0199"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Petar Sirkovi\u0107","raw_affiliation_strings":["Chair of Numerical Algorithms and HPC MATHICSE, EPF Lausanne  CH\u20101015 Lausanne Switzerland","Chair of Numerical Algorithms and HPC, MATHICSE, EPF Lausanne, CH-1015 Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Chair of Numerical Algorithms and HPC MATHICSE, EPF Lausanne  CH\u20101015 Lausanne Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Chair of Numerical Algorithms and HPC, MATHICSE, EPF Lausanne, CH-1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5048101802"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":2.9108,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.91422207,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"22","issue":"3","first_page":"564","last_page":"583"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991000294685364,"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":0.9991000294685364,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.998199999332428,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8187786340713501},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.7694871425628662},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6846343278884888},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.6568762063980103},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.6271757483482361},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6150338649749756},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.5973473191261292},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5712773203849792},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.48898041248321533},{"id":"https://openalex.org/keywords/numerical-linear-algebra","display_name":"Numerical linear algebra","score":0.4676468074321747},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.4660424292087555},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.43827494978904724},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2980400323867798},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2090284824371338},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20379233360290527},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19942915439605713},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.17395305633544922},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.10641622543334961}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8187786340713501},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.7694871425628662},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6846343278884888},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.6568762063980103},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.6271757483482361},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6150338649749756},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.5973473191261292},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5712773203849792},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.48898041248321533},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.4676468074321747},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4660424292087555},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.43827494978904724},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2980400323867798},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2090284824371338},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20379233360290527},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19942915439605713},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.17395305633544922},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.10641622543334961},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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":3,"locations":[{"id":"doi:10.1002/nla.1973","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.1973","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:208146","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/208146","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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":"","raw_type":"Text"},{"id":"pmh:oai:infoscience.tind.io:208146","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/114222","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:208146","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/208146","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3770479564","display_name":null,"funder_award_id":"200021_138041","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W25664821","https://openalex.org/W1520511539","https://openalex.org/W1895683009","https://openalex.org/W1976986637","https://openalex.org/W1996869553","https://openalex.org/W2000630868","https://openalex.org/W2002858896","https://openalex.org/W2016075148","https://openalex.org/W2030679798","https://openalex.org/W2034274983","https://openalex.org/W2034590496","https://openalex.org/W2057577185","https://openalex.org/W2060200773","https://openalex.org/W2066009815","https://openalex.org/W2068314547","https://openalex.org/W2069070178","https://openalex.org/W2088087394","https://openalex.org/W2089099479","https://openalex.org/W2090696580","https://openalex.org/W2090963365","https://openalex.org/W2091160474","https://openalex.org/W2119354869","https://openalex.org/W2131771606","https://openalex.org/W2136556155","https://openalex.org/W2137874355","https://openalex.org/W2162144261","https://openalex.org/W2169328438","https://openalex.org/W2259201661","https://openalex.org/W2465088004","https://openalex.org/W2480611454","https://openalex.org/W2963858059"],"related_works":["https://openalex.org/W3097421206","https://openalex.org/W2048286546","https://openalex.org/W2506892714","https://openalex.org/W2037819582","https://openalex.org/W2349379571","https://openalex.org/W2980165407","https://openalex.org/W2365527693","https://openalex.org/W2550490477","https://openalex.org/W3208358470","https://openalex.org/W2046729504"],"abstract_inverted_index":{"Summary":[0],"This":[1],"work":[2],"is":[3],"concerned":[4],"with":[5,69],"the":[6,21,34,51,98,101,126,137],"numerical":[7],"solution":[8,22],"of":[9,23,37,80,100,139],"large\u2010scale":[10],"linear":[11,30,78,95,108],"matrix":[12,109],"equations":[13,110],".":[14],"The":[15],"most":[16],"straightforward":[17],"approach":[18,49],"computes":[19],"from":[20],"an":[24],"m":[25,28,38,82,84,114],"n":[26,29,40,86,88,116],"\u00d7":[27,83,87],"system,":[31],"typically":[32],"limiting":[33],"feasible":[35],"values":[36],",":[39],"to":[41,90,106,153],"a":[42,61],"few":[43],"hundreds":[44],"at":[45],"most.":[46],"Our":[47],"new":[48],"exploits":[50],"fact":[52],"that":[53,125,155],"X":[54],"can":[55,145],"often":[56],"be":[57,91,146],"well":[58,130],"approximated":[59],"by":[60],"low\u2010rank":[62,67],"matrix.":[63],"It":[64],"combines":[65],"greedy":[66],"techniques":[68],"Galerkin":[70],"projection":[71],"and":[72,85],"preconditioned":[73],"gradients.":[74],"In":[75],"turn,":[76],"only":[77],"systems":[79,96],"size":[81],"need":[89,152],"solved.":[92],"Moreover,":[93],"these":[94],"inherit":[97],"sparsity":[99],"coefficient":[102],"matrices,":[103],"which":[104],"allows":[105],"address":[107],"as":[111,113,148],"large":[112],"=":[115,117],"O":[118],"(10":[119],"5":[120],").":[121],"Numerical":[122],"experiments":[123],"demonstrate":[124],"proposed":[127],"methods":[128,144],"perform":[129],"for":[131,136],"generalized":[132],"Lyapunov":[133,141],"equations.":[134],"Even":[135],"case":[138],"standard":[140],"equations,":[142],"our":[143],"advantageous,":[147],"we":[149],"do":[150],"not":[151],"assume":[154],"C":[156],"has":[157],"low":[158],"rank.":[159],"Copyright":[160],"\u00a9":[161],"2015":[162],"John":[163],"Wiley":[164],"&":[165],"Sons,":[166],"Ltd.":[167]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}