{"id":"https://openalex.org/W2032604276","doi":"https://doi.org/10.1002/1099-1506(200101/02)8:1<53::aid-nla228>3.0.co;2-3","title":"Nonequivalence transformation of?-matrix eigenproblems and model embedding approach to model tuning","display_name":"Nonequivalence transformation of?-matrix eigenproblems and model embedding approach to model tuning","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2032604276","doi":"https://doi.org/10.1002/1099-1506(200101/02)8:1<53::aid-nla228>3.0.co;2-3","mag":"2032604276"},"language":"en","primary_location":{"id":"doi:10.1002/1099-1506(200101/02)8:1<53::aid-nla228>3.0.co;2-3","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1099-1506(200101/02)8:1<53::aid-nla228>3.0.co;2-3","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033152410","display_name":"William R. Ferng","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"William R. Ferng","raw_affiliation_strings":["Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan","Department of Applied Mathematics National Chiao Tung University Hsinchu 30050, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan","institution_ids":["https://openalex.org/I148366613"]},{"raw_affiliation_string":"Department of Applied Mathematics National Chiao Tung University Hsinchu 30050, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110004104","display_name":"Wen-Wei Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Wen-Wei Lin","raw_affiliation_strings":["Department of Mathematics, National Tsing Hua University, Hsinchu 30043, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Tsing Hua University, Hsinchu 30043, Taiwan","institution_ids":["https://openalex.org/I25846049"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091903326","display_name":"Daniel J. Pierce","orcid":null},"institutions":[{"id":"https://openalex.org/I2801120396","display_name":"Boeing (Australia)","ror":"https://ror.org/0346ase89","country_code":"AU","type":"company","lineage":["https://openalex.org/I1295339012","https://openalex.org/I2801120396"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Daniel J. Pierce","raw_affiliation_strings":["Boeing Shared Services, P.O. Box 3707, MC 7L-22, Seattle, WA 98124-2207, U.S.A","Boeing"],"affiliations":[{"raw_affiliation_string":"Boeing Shared Services, P.O. Box 3707, MC 7L-22, Seattle, WA 98124-2207, U.S.A","institution_ids":[]},{"raw_affiliation_string":"Boeing","institution_ids":["https://openalex.org/I2801120396"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028142943","display_name":"Chern-Shuh Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I91807558","display_name":"National Cheng Kung University","ror":"https://ror.org/01b8kcc49","country_code":"TW","type":"education","lineage":["https://openalex.org/I91807558"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chern-Shuh Wang","raw_affiliation_strings":["Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan","Department of Mathematics, National Cheng Kung University, Tainan, 701, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan","institution_ids":["https://openalex.org/I91807558"]},{"raw_affiliation_string":"Department of Mathematics, National Cheng Kung University, Tainan, 701, Taiwan","institution_ids":["https://openalex.org/I91807558"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5033152410"],"corresponding_institution_ids":["https://openalex.org/I148366613"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":0.9084,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.75233499,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"8","issue":"1","first_page":"53","last_page":"70"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9984999895095825,"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":0.9984999895095825,"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/T13126","display_name":"Scientific Research and Discoveries","score":0.9976000189781189,"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/T11236","display_name":"Control Systems and Identification","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7892378568649292},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.7741405963897705},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7385440468788147},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.6492334008216858},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5682871341705322},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5539469122886658},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5398700833320618},{"id":"https://openalex.org/keywords/flexibility","display_name":"Flexibility (engineering)","score":0.4858843684196472},{"id":"https://openalex.org/keywords/transformation-matrix","display_name":"Transformation matrix","score":0.4743332266807556},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4659961462020874},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.44816023111343384},{"id":"https://openalex.org/keywords/eigendecomposition-of-a-matrix","display_name":"Eigendecomposition of a matrix","score":0.4255278408527374},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3698808252811432},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.338525652885437},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19160732626914978},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07105851173400879}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7892378568649292},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7741405963897705},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7385440468788147},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.6492334008216858},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5682871341705322},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5539469122886658},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5398700833320618},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.4858843684196472},{"id":"https://openalex.org/C165443888","wikidata":"https://www.wikidata.org/wiki/Q1482183","display_name":"Transformation matrix","level":3,"score":0.4743332266807556},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4659961462020874},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44816023111343384},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.4255278408527374},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3698808252811432},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.338525652885437},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19160732626914978},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07105851173400879},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/1099-1506(200101/02)8:1<53::aid-nla228>3.0.co;2-3","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1099-1506(200101/02)8:1<53::aid-nla228>3.0.co;2-3","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","score":0.6100000143051147,"display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306077","display_name":"Boeing","ror":"https://ror.org/04sm5zn07"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W135863185","https://openalex.org/W330372241","https://openalex.org/W391578156","https://openalex.org/W583311967","https://openalex.org/W1967890524","https://openalex.org/W2077950830","https://openalex.org/W2092417254","https://openalex.org/W2124986435","https://openalex.org/W2156494024","https://openalex.org/W2170598631","https://openalex.org/W2610857016","https://openalex.org/W2754483884","https://openalex.org/W6605491818","https://openalex.org/W6611481880","https://openalex.org/W6820064201"],"related_works":["https://openalex.org/W2081900870","https://openalex.org/W2183306018","https://openalex.org/W2549990292","https://openalex.org/W2345479200","https://openalex.org/W2951819827","https://openalex.org/W2849310602","https://openalex.org/W2419146053","https://openalex.org/W2088247287","https://openalex.org/W3006008237","https://openalex.org/W2470850800"],"abstract_inverted_index":{"In":[0],"this":[1,19],"paper":[2],"we":[3],"present":[4],"some":[5],"theory":[6],"for":[7,14,24],"a":[8,28,50],"non-equivalence":[9],"transformation":[10,20],"of":[11,18],"matrix":[12],"eigenvalues":[13],"\u03bb-matrix":[15],"polynomials.":[16],"Application":[17],"to":[21],"eigenvalue":[22],"embedding":[23],"model":[25],"tuning":[26],"on":[27,49],"realistic":[29],"industry":[30],"problem":[31],"is":[32,58],"illustrated.":[33],"The":[34,55],"new":[35],"approach":[36],"has":[37],"several":[38],"advantages":[39],"such":[40],"as":[41],"flexibility,":[42],"efficiency,":[43],"and":[44],"structure-preservation.":[45],"A":[46],"numerical":[47],"experiment":[48],"pseudosimulation":[51],"data":[52],"set":[53],"from":[54],"Boeing":[56],"Company":[57],"reported.":[59],"Copyright":[60],"\u00a9":[61],"2001":[62],"John":[63],"Wiley":[64],"&":[65],"Sons,":[66],"Ltd.":[67]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
