{"id":"https://openalex.org/W2071045420","doi":"https://doi.org/10.1137/s0895479893252337","title":"Least-Squares Approximate Solution of Overdetermined Sylvester Equations","display_name":"Least-Squares Approximate Solution of Overdetermined Sylvester Equations","publication_year":1997,"publication_date":"1997-04-01","ids":{"openalex":"https://openalex.org/W2071045420","doi":"https://doi.org/10.1137/s0895479893252337","mag":"2071045420"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479893252337","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479893252337","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113594860","display_name":"A.S. Hodel","orcid":null},"institutions":[{"id":"https://openalex.org/I19648265","display_name":"Wright State University","ror":"https://ror.org/04qk6pt94","country_code":"US","type":"education","lineage":["https://openalex.org/I19648265"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. Scottedward Hodel","raw_affiliation_strings":["Wright State University;"],"affiliations":[{"raw_affiliation_string":"Wright State University;","institution_ids":["https://openalex.org/I19648265"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043862324","display_name":"Pradeep Kumar M\u0131sra","orcid":"https://orcid.org/0000-0002-9164-6071"},"institutions":[{"id":"https://openalex.org/I19648265","display_name":"Wright State University","ror":"https://ror.org/04qk6pt94","country_code":"US","type":"education","lineage":["https://openalex.org/I19648265"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pradeep Misra","raw_affiliation_strings":["Wright State University;"],"affiliations":[{"raw_affiliation_string":"Wright State University;","institution_ids":["https://openalex.org/I19648265"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113594860"],"corresponding_institution_ids":["https://openalex.org/I19648265"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.18925926,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"18","issue":"2","first_page":"279","last_page":"290"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9936000108718872,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/overdetermined-system","display_name":"Overdetermined system","score":0.9577721953392029},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8402597308158875},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.5903910994529724},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.584307074546814},{"id":"https://openalex.org/keywords/sylvester-equation","display_name":"Sylvester equation","score":0.5498261451721191},{"id":"https://openalex.org/keywords/sylvester-matrix","display_name":"Sylvester matrix","score":0.5306771397590637},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5275311470031738},{"id":"https://openalex.org/keywords/linear-least-squares","display_name":"Linear least squares","score":0.5266699194908142},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.48705723881721497},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45478782057762146},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.44057056307792664},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4180954098701477},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2980618178844452},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2768245339393616},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20374080538749695},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.19212543964385986},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1006033718585968},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06796503067016602}],"concepts":[{"id":"https://openalex.org/C81901731","wikidata":"https://www.wikidata.org/wiki/Q331348","display_name":"Overdetermined system","level":2,"score":0.9577721953392029},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8402597308158875},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.5903910994529724},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.584307074546814},{"id":"https://openalex.org/C100468782","wikidata":"https://www.wikidata.org/wiki/Q3730848","display_name":"Sylvester equation","level":3,"score":0.5498261451721191},{"id":"https://openalex.org/C20160815","wikidata":"https://www.wikidata.org/wiki/Q1482452","display_name":"Sylvester matrix","level":5,"score":0.5306771397590637},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5275311470031738},{"id":"https://openalex.org/C58663186","wikidata":"https://www.wikidata.org/wiki/Q6553462","display_name":"Linear least squares","level":3,"score":0.5266699194908142},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.48705723881721497},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45478782057762146},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.44057056307792664},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4180954098701477},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2980618178844452},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2768245339393616},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20374080538749695},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.19212543964385986},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1006033718585968},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06796503067016602},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.0},{"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/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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.0},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0895479893252337","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479893252337","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:corescholar.libraries.wright.edu:ee-1003","is_oa":false,"landing_page_url":"https://corescholar.libraries.wright.edu/ee/2","pdf_url":null,"source":{"id":"https://openalex.org/S2737205702","display_name":"Journal of Bioresource Management","issn_l":"2309-3854","issn":["2309-3854"],"is_oa":false,"is_in_doaj":true,"is_core":false,"host_organization":"https://openalex.org/P4310316536","host_organization_name":"Bioresource Research Center (BRC), Islamabad","host_organization_lineage":["https://openalex.org/P4310316536"],"host_organization_lineage_names":["Bioresource Research Center (BRC), Islamabad"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Electrical Engineering Faculty Publications","raw_type":"text"},{"id":"pmh:oai:works.bepress.com:pradeep_misra-1001","is_oa":false,"landing_page_url":"https://works.bepress.com/pradeep_misra/2","pdf_url":null,"source":{"id":"https://openalex.org/S2737205702","display_name":"Journal of Bioresource Management","issn_l":"2309-3854","issn":["2309-3854"],"is_oa":false,"is_in_doaj":true,"is_core":false,"host_organization":"https://openalex.org/P4310316536","host_organization_name":"Bioresource Research Center (BRC), Islamabad","host_organization_lineage":["https://openalex.org/P4310316536"],"host_organization_lineage_names":["Bioresource Research Center (BRC), Islamabad"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Pradeep Misra","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G275884281","display_name":"Research Initiation Award:  Numerical Methods for Control   System Design Involving Large Dimensional Systems","funder_award_id":"9110083","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":31,"referenced_works":["https://openalex.org/W26572052","https://openalex.org/W845130065","https://openalex.org/W1854226152","https://openalex.org/W1969626918","https://openalex.org/W1975194844","https://openalex.org/W1984230747","https://openalex.org/W1991485997","https://openalex.org/W1997974102","https://openalex.org/W1998591070","https://openalex.org/W2000630868","https://openalex.org/W2011439311","https://openalex.org/W2033029203","https://openalex.org/W2035387301","https://openalex.org/W2036191408","https://openalex.org/W2040566538","https://openalex.org/W2042255949","https://openalex.org/W2054689585","https://openalex.org/W2064733273","https://openalex.org/W2088748973","https://openalex.org/W2095590702","https://openalex.org/W2097660079","https://openalex.org/W2109272761","https://openalex.org/W2110021831","https://openalex.org/W2110451173","https://openalex.org/W2123783510","https://openalex.org/W2139875628","https://openalex.org/W2140153041","https://openalex.org/W2143588898","https://openalex.org/W2166904966","https://openalex.org/W2316564661","https://openalex.org/W2798909945"],"related_works":["https://openalex.org/W1973485705","https://openalex.org/W2087190655","https://openalex.org/W1597114477","https://openalex.org/W2036701498","https://openalex.org/W2104785239","https://openalex.org/W2068124938","https://openalex.org/W4308495437","https://openalex.org/W2502651484","https://openalex.org/W2964330793","https://openalex.org/W2071045420"],"abstract_inverted_index":{"We":[0],"address":[1],"the":[2,11,15,29,39,43,57,62,66,80,88,93,105,110],"problem":[3,34],"of":[4,10,14,45,61,87,92],"computing":[5,28],"a":[6,53],"low-rank":[7,76],"estimate":[8,85],"Y":[9,113],"solution":[12,60,78,90],"X":[13,19,21,31,91],"Lyapunov":[16,63,94],"equation":[17,64],"A":[18],"+":[20,23,114,117],"A'":[22],"Q":[24],"=":[25],"0":[26],"without":[27],"matrix":[30,106],"itself.":[32],"This":[33],"has":[35],"applications":[36],"in":[37,52],"both":[38],"reduced-order":[40],"modeling":[41],"and":[42],"control":[44],"large":[46],"dimensional":[47],"systems":[48],"as":[49,51],"well":[50],"hybrid":[54],"algorithm":[55],"for":[56,75,103],"rapid":[58],"numerical":[59],"via":[65],"alternating":[67],"direction":[68],"implicit":[69],"method.":[70],"While":[71],"no":[72],"known":[73],"methods":[74],"approximate":[77],"provide":[79,99],"two-norm":[81],"optimal":[82],"rank":[83],"k":[84],"Xk":[86,107],"exact":[89],"equation,":[95],"our":[96],"iterative":[97],"algorithms":[98],"an":[100],"effective":[101],"method":[102],"estimating":[104],"by":[108],"minimizing":[109],"error":[111],"||A":[112],"YA":[115],"'":[116],"Q||F.":[118]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
