{"id":"https://openalex.org/W7167797918","doi":"https://doi.org/10.48550/arxiv.2607.07440","title":"Compact Rational Krylov for Parametrized Systems with Application to BEM Frequency Sweeping","display_name":"Compact Rational Krylov for Parametrized Systems with Application to BEM Frequency Sweeping","publication_year":2026,"publication_date":"2026-07-08","ids":{"openalex":"https://openalex.org/W7167797918","doi":"https://doi.org/10.48550/arxiv.2607.07440"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.07440","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.07440","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.07440","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5098903342","display_name":"Kobe Bruyninckx","orcid":"https://orcid.org/0000-0003-2063-2948"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bruyninckx, Kobe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022994939","display_name":"Daan Huybrechs","orcid":"https://orcid.org/0000-0002-0536-2647"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huybrechs, Daan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5079388991","display_name":"Karl Meerbergen","orcid":"https://orcid.org/0000-0002-1508-0248"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Meerbergen, Karl","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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":0.8349000215530396,"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":0.8349000215530396,"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":0.07349999994039536,"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/T12303","display_name":"Tensor decomposition and applications","score":0.02239999920129776,"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/linear-system","display_name":"Linear system","score":0.6935999989509583},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.6920999884605408},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5134000182151794},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.5034999847412109},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.48010000586509705},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.47940000891685486},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4507000148296356},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4503999948501587}],"concepts":[{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.6935999989509583},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.6920999884605408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6262999773025513},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5198000073432922},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5134000182151794},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.5034999847412109},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48010000586509705},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.47940000891685486},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4507000148296356},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4503999948501587},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.41909998655319214},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.39570000767707825},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.3695000112056732},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.3495999872684479},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3109000027179718},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.30820000171661377},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.29589998722076416},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.2824000120162964},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2808000147342682},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27140000462532043},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2703000009059906},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.26010000705718994}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.07440","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.07440","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,"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.07440","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.07440","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,"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"},"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":{"In":[0,61,92],"parametrized":[1,65,96],"linear":[2,75,90,97],"systems":[3],"$\\mathsf{P}(\u03bc)\\mathsf{x}=\\mathsf{b}$":[4],"the":[5,28,57,64,93,102,105,111,121,125,128,144,149,165,172,180,191],"system":[6,52,66,76,196],"matrix":[7],"$\\mathsf{P}$":[8],"depends":[9,142],"nonlinearly":[10],"on":[11,120,143],"a":[12,51,72,80,136],"parameter":[13,58],"$\u03bc$":[14],"and":[15,82,107,115,154],"solutions":[16,48],"are":[17],"sought":[18],"for":[19,53,88,158],"many":[20,54],"values":[21,55],"of":[22,56,95,127,175,190],"this":[23,62],"parameter.":[24],"We":[25,78],"show":[26,132],"that":[27,140],"compact":[29],"rational":[30,84],"Krylov":[31,85],"(CORK)":[32],"framework,":[33,113],"originally":[34],"introduced":[35],"to":[36,44,49,134,147,151,156],"solve":[37],"nonlinear":[38],"eigenvalue":[39],"problems,":[40],"can":[41,100],"be":[42],"used":[43],"efficiently":[45],"produce":[46],"approximate":[47],"such":[50],"at":[59,161],"once.":[60],"approach,":[63],"is":[67],"first":[68],"linearized,":[69],"resulting":[70],"in":[71,104,108],"large":[73],"shifted":[74,89],"$(\\boldsymbol{\\mathsf{A}}-\u03bc\\boldsymbol{\\mathsf{B}})\\boldsymbol{\\mathsf{y}}=\\boldsymbol{\\mathsf{d}}$.":[77],"formulate":[79],"left-":[81],"right-preconditioned":[83],"GMRES":[86],"method":[87],"systems.":[91],"setting":[94],"systems,":[98],"these":[99,162],"exploit":[101],"structure":[103],"linearization,":[106],"combination":[109],"with":[110],"CORK":[112],"computational":[114],"memory":[116],"complexity":[117],"mainly":[118],"depend":[119],"problem":[122],"size,":[123],"less":[124],"degree":[126],"linearization.":[129],"Additionally,":[130],"we":[131,170],"how":[133,146,155],"incorporate":[135],"right-hand":[137],"side":[138],"$\\mathsf{b}(\u03bc)$":[139],"also":[141],"parameter,":[145],"choose":[148],"shifts":[150,163],"steer":[152],"convergence":[153],"allow":[157],"inexact":[159],"solves":[160],"throughout":[164],"iterations.":[166],"As":[167],"an":[168,187],"application":[169],"consider":[171],"'frequency":[173],"sweeping'":[174],"Helmholtz":[176],"scattering":[177],"problems":[178],"through":[179],"Boundary":[181],"Element":[182],"Method":[183],"(BEM),":[184],"enabled":[185],"via":[186],"efficient":[188],"representation":[189],"dense":[192],"but":[193],"data-sparse":[194],"wavenumber-dependent":[195],"matrix.":[197]},"counts_by_year":[],"updated_date":"2026-08-08T07:41:36.138363","created_date":"2026-07-10T00:00:00"}
