{"id":"https://openalex.org/W7203900101","doi":"https://doi.org/10.48550/arxiv.2608.19818","title":"Eigensolvers for polynomial roots and tensor decomposition","display_name":"Eigensolvers for polynomial roots and tensor decomposition","publication_year":2026,"publication_date":"2026-08-20","ids":{"openalex":"https://openalex.org/W7203900101","doi":"https://doi.org/10.48550/arxiv.2608.19818"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.19818","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.19818","pdf_url":"https://arxiv.org/pdf/2608.19818","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.19818","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120654807","display_name":"Enrica Barrilli","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4405260808","display_name":"AROMATH: Algebre geometrie Modelisation et Algorithmes","ror":"https://ror.org/04a11tk94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210106545","https://openalex.org/I4405260808"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Barrilli, Enrica","raw_affiliation_strings":["AROMATH"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AROMATH","institution_ids":["https://openalex.org/I4405260808"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003683965","display_name":"Bernard Mourrain","orcid":"https://orcid.org/0000-0002-8813-1368","observed_orcids":["https://orcid.org/0000-0002-8813-1368"]},"institutions":[{"id":"https://openalex.org/I4405260808","display_name":"AROMATH: Algebre geometrie Modelisation et Algorithmes","ror":"https://ror.org/04a11tk94","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210106545","https://openalex.org/I4405260808"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mourrain, Bernard","raw_affiliation_strings":["AROMATH"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AROMATH","institution_ids":["https://openalex.org/I4405260808"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4405260808"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9696999788284302,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9696999788284302,"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/T12303","display_name":"Tensor decomposition and applications","score":0.027300000190734863,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.0006000000284984708,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenvalue-solvers","display_name":"eigensolvers","score":0.7730000019073486},{"id":"https://openalex.org/keywords/polynomial-root-finding","display_name":"polynomial root finding","score":0.7570000290870667},{"id":"https://openalex.org/keywords/tensor-decomposition","display_name":"tensor decomposition","score":0.9480000138282776},{"id":"https://openalex.org/keywords/commuting-operators","display_name":"commuting operators","score":0.9089999794960022},{"id":"https://openalex.org/keywords/symbolic-numeric-computation","display_name":"symbolic-numeric computation","score":0.7409999966621399},{"id":"https://openalex.org/keywords/eigenvalue-multiplicity","display_name":"eigenvalue multiplicity","score":0.8939999938011169}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7986000180244446},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6484000086784363},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5231999754905701},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.5051000118255615},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4984999895095825},{"id":"https://openalex.org/C2986737658","wikidata":"https://www.wikidata.org/wiki/Q30103009","display_name":"Tensor decomposition","level":3,"score":0.47519999742507935},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.47200000286102295},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4659999907016754},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4390000104904175},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.43529999256134033},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.38499999046325684},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.3662000000476837},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.3327000141143799},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.3149999976158142},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.296999990940094},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.29589998722076416},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.287200003862381},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2759000062942505},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.27390000224113464},{"id":"https://openalex.org/C18555067","wikidata":"https://www.wikidata.org/wiki/Q8375051","display_name":"Joint (building)","level":2,"score":0.27379998564720154},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.26510000228881836},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25870001316070557},{"id":"https://openalex.org/C73772418","wikidata":"https://www.wikidata.org/wiki/Q6888018","display_name":"Modal matrix","level":5,"score":0.257999986410141},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25589999556541443},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.2513999938964844}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2608.19818","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.19818","pdf_url":"https://arxiv.org/pdf/2608.19818","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-05711493v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05711493","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"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":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:HAL:hal-05711493v2","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05711493v2/document","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"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":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2608.19818","doi":"https://doi.org/10.48550/arxiv.2608.19818","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.19818","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.19818","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.19818","pdf_url":"https://arxiv.org/pdf/2608.19818","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1011636513","display_name":null,"funder_award_id":"HORIZON-MSCA-2023-DN","funder_id":"https://openalex.org/F4320334322","funder_display_name":"HORIZON EUROPE Framework Programme"},{"id":"https://openalex.org/G5145581018","display_name":null,"funder_award_id":"101120296","funder_id":"https://openalex.org/F4320338337","funder_display_name":"H2020 Marie Sk\u0142odowska-Curie Actions"},{"id":"https://openalex.org/G5160414380","display_name":null,"funder_award_id":"101120296","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334322","display_name":"HORIZON EUROPE Framework Programme","ror":null},{"id":"https://openalex.org/F4320338337","display_name":"H2020 Marie Sk\u0142odowska-Curie Actions","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203900101.pdf","grobid_xml":"https://content.openalex.org/works/W7203900101.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4366198147"],"related_works":["https://openalex.org/W3174231256","https://openalex.org/W2101011523","https://openalex.org/W2161492410","https://openalex.org/W4232270347","https://openalex.org/W3163796952","https://openalex.org/W7097582144","https://openalex.org/W2135960888","https://openalex.org/W7095298571","https://openalex.org/W6990283842","https://openalex.org/W2788821003"],"abstract_inverted_index":{"Computing":[0],"eigenvalues":[1],"and":[2,52,73],"eigenvectors":[3,27,69],"is":[4],"at":[5],"the":[6,9,18,39,45,48,58,65,85],"heart":[7],"of":[8,11,20,28,30,42,44,47,60,67,70],"solution":[10],"many":[12],"non-linear":[13],"problems.":[14],"For":[15],"instance,":[16],"finding":[17],"roots":[19],"polynomial":[21],"systems":[22],"reduces":[23],"to":[24],"computing":[25,57],"joint":[26,40,68],"operators":[29],"multiplication.":[31],"Similarly,":[32],"tensor":[33],"decomposition":[34],"can":[35],"be":[36],"performed":[37],"via":[38],"diagonalization":[41],"submatrices":[43],"Catalecticant":[46],"tensor.":[49],"We":[50],"describe":[51],"illustrate":[53],"symbolic-numeric":[54],"methods":[55],"for":[56,74],"solutions":[59],"these":[61],"algebraic":[62],"problems":[63],"from":[64],"computation":[66],"commuting":[71],"operators,":[72],"analysing":[75],"their":[76,82],"multiplicity":[77],"structure,":[78],"as":[79,81],"well":[80],"implementation":[83],"in":[84],"package":[86],"AlgebraicSolvers.jl.":[87]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-22T00:00:00"}