{"id":"https://openalex.org/W7138248446","doi":"https://doi.org/10.48550/arxiv.2603.13794","title":"NEP_MiniMax: An Approach for NEPs Based on Matrix-valued Minimax Approximations","display_name":"NEP_MiniMax: An Approach for NEPs Based on Matrix-valued Minimax Approximations","publication_year":2026,"publication_date":"2026-03-14","ids":{"openalex":"https://openalex.org/W7138248446","doi":"https://doi.org/10.48550/arxiv.2603.13794"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.13794","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.13794","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.13794","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5129681114","display_name":"Chenkun Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Chenkun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124053214","display_name":"Jiawei Gu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gu, Jiawei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5129696897","display_name":"Lei-Hong Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Lei-Hong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.3061999976634979,"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":0.3061999976634979,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.25600001215934753,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.12300000339746475,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/minimax","display_name":"Minimax","score":0.8676999807357788},{"id":"https://openalex.org/keywords/minimax-approximation-algorithm","display_name":"Minimax approximation algorithm","score":0.7943000197410583},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.7498999834060669},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6186000108718872},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.5162000060081482},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.503600001335144},{"id":"https://openalex.org/keywords/approximation-theory","display_name":"Approximation theory","score":0.4966999888420105},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.48899999260902405},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4871000051498413}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.8676999807357788},{"id":"https://openalex.org/C117148685","wikidata":"https://www.wikidata.org/wiki/Q6865376","display_name":"Minimax approximation algorithm","level":2,"score":0.7943000197410583},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.7498999834060669},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7031000256538391},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6186000108718872},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5162000060081482},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.503600001335144},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.4966999888420105},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.48899999260902405},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4871000051498413},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4796999990940094},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.46939998865127563},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45399999618530273},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.4487000107765198},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4309999942779541},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4083999991416931},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.37369999289512634},{"id":"https://openalex.org/C160824197","wikidata":"https://www.wikidata.org/wiki/Q2071054","display_name":"Linear approximation","level":3,"score":0.36809998750686646},{"id":"https://openalex.org/C9353750","wikidata":"https://www.wikidata.org/wiki/Q5384549","display_name":"Equioscillation theorem","level":5,"score":0.3677000105381012},{"id":"https://openalex.org/C138029060","wikidata":"https://www.wikidata.org/wiki/Q7226633","display_name":"Polynomial and rational function modeling","level":3,"score":0.3393000066280365},{"id":"https://openalex.org/C62376455","wikidata":"https://www.wikidata.org/wiki/Q935210","display_name":"Spouge's approximation","level":3,"score":0.3043999969959259},{"id":"https://openalex.org/C99140742","wikidata":"https://www.wikidata.org/wiki/Q843550","display_name":"Polynomial-time approximation scheme","level":3,"score":0.29350000619888306},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C142311740","wikidata":"https://www.wikidata.org/wiki/Q1066177","display_name":"Shaping","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C2780861221","wikidata":"https://www.wikidata.org/wiki/Q913849","display_name":"Minimax theorem","level":3,"score":0.25589999556541443}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.13794","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.13794","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.13794","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.13794","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"propose":[1],"NEP_MiniMax,":[2],"a":[3,27,37,50,61,84,92],"novel":[4],"computational":[5],"method":[6,21],"for":[7,41],"solving":[8,83],"nonlinear":[9],"eigenvalue":[10,86,98],"problems":[11],"(NEPs)":[12],"$T(\u03bb)\\mathbf{u}=":[13],"0$":[14,90],"on":[15,102],"compact":[16],"continua":[17],"$\u03a9\\subset":[18],"\\mathbb{C}$.":[19],"The":[20,65],"combines":[22],"two":[23],"key":[24],"components:":[25],"(1)":[26],"rational":[28,39,52,131],"minimax":[29,38,66],"approximation":[30,40,53,67,132],"scheme":[31],"where":[32],"the":[33,42,105,130],"{m-d-Lawson}":[34],"algorithm":[35],"constructs":[36],"vector-valued":[43],"function":[44],"from":[45,104],"$T(x)$'s":[46],"split":[47],"form,":[48],"yielding":[49],"matrix-valued":[51],"$R^*(x)":[54],"=":[55],"P^*(x)/q^*(x)":[56],"\\approx":[57],"T(x)$,":[58],"and":[59,119],"(2)":[60],"structure-exploiting":[62],"linearization":[63,94],"technique.":[64],"guarantees":[68],"uniform":[69],"accuracy":[70],"while":[71],"generally":[72],"keeping":[73],"$R^*(x)$":[74],"pole-free":[75],"in":[76,117],"$\u03a9$.":[77],"Eigenpairs":[78],"are":[79],"then":[80],"computed":[81],"by":[82],"polynomial":[85],"problem":[87],"$P^*(\u03bb)":[88],"\\mathbf{u}=":[89],"via":[91],"strong":[93],"that":[95],"exactly":[96],"preserves":[97],"multiplicities.":[99],"Numerical":[100],"experiments":[101],"benchmarks":[103],"NLEVP":[106],"collection":[107],"demonstrate":[108],"competitiveness":[109],"with":[110,121],"state-of-the-art":[111],"methods":[112],"(e.g.,":[113],"Beyn,":[114],"NLEIGS,":[115],"SV-AAA)":[116],"efficiency":[118],"accuracy,":[120],"theoretical":[122],"error":[123],"bounds":[124],"directly":[125],"relating":[126],"eigenpair":[127],"approximations":[128],"to":[129],"quality.":[133]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-18T00:00:00"}