{"id":"https://openalex.org/W2809427435","doi":"https://doi.org/10.1137/18m1202323","title":"Efficient Solution of Symmetric Eigenvalue Problems from Families of Coupled Systems","display_name":"Efficient Solution of Symmetric Eigenvalue Problems from Families of Coupled Systems","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2809427435","doi":"https://doi.org/10.1137/18m1202323","mag":"2809427435"},"language":"en","primary_location":{"id":"doi:10.1137/18m1202323","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1202323","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1806.07235","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059012423","display_name":"Antti Hannukainen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Antti Hannukainen","raw_affiliation_strings":["Department of Mathematics and Systems Analysis"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Systems Analysis","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081417088","display_name":"Jarmo Malinen","orcid":"https://orcid.org/0000-0001-9117-8450"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jarmo Malinen","raw_affiliation_strings":["Department of Mathematics and Systems Analysis"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Systems Analysis","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018786747","display_name":"Antti Ojalammi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Antti Ojalammi","raw_affiliation_strings":["Department of Mathematics and Systems Analysis"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Systems Analysis","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00155067,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"57","issue":"4","first_page":"1789","last_page":"1814"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12435","display_name":"Bladed Disk Vibration Dynamics","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/mathematics","display_name":"Mathematics","score":0.7199963927268982},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.669696569442749},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5962756276130676},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5866074562072754},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49754074215888977},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.48469260334968567},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.47995737195014954},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.47748658061027527},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47685396671295166},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43805965781211853},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19659370183944702},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17834687232971191},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12188497185707092},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08834415674209595}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7199963927268982},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.669696569442749},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5962756276130676},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5866074562072754},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49754074215888977},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.48469260334968567},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.47995737195014954},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.47748658061027527},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47685396671295166},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43805965781211853},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19659370183944702},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17834687232971191},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12188497185707092},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08834415674209595},{"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/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/18m1202323","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1202323","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1806.07235","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.07235","pdf_url":"https://arxiv.org/pdf/1806.07235","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2809427435","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1806.07235.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:aaltodoc.aalto.fi:123456789/40598","is_oa":true,"landing_page_url":"https://research.aalto.fi/en/publications/f32feeb5-330f-446f-b158-110bad7683c6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401663","display_name":"Aaltodoc (Aalto University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9927081","host_organization_name":"Aalto University","host_organization_lineage":["https://openalex.org/I9927081"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"doi:10.48550/arxiv.1806.07235","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1806.07235","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":"pmh:oai:arXiv.org:1806.07235","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.07235","pdf_url":"https://arxiv.org/pdf/1806.07235","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4663284557","display_name":null,"funder_award_id":"312340","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"}],"funders":[{"id":"https://openalex.org/F4320321108","display_name":"Academy of Finland","ror":"https://ror.org/05k73zm37"},{"id":"https://openalex.org/F4320322400","display_name":"Magnus Ehrnroothin S\u00e4\u00e4ti\u00f6","ror":"https://ror.org/02cdzet69"},{"id":"https://openalex.org/F4320327217","display_name":"Siemens Healthineers","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1887796341","https://openalex.org/W1981792545","https://openalex.org/W1988662661","https://openalex.org/W1992443231","https://openalex.org/W2012199071","https://openalex.org/W2023576489","https://openalex.org/W2032802290","https://openalex.org/W2036215846","https://openalex.org/W2036668588","https://openalex.org/W2041613966","https://openalex.org/W2044752794","https://openalex.org/W2059586807","https://openalex.org/W2086987344","https://openalex.org/W2094766891","https://openalex.org/W2114592516","https://openalex.org/W2118307706","https://openalex.org/W2118357359","https://openalex.org/W2134586925","https://openalex.org/W2157129549","https://openalex.org/W2174300045","https://openalex.org/W2185923856","https://openalex.org/W2467346979","https://openalex.org/W2508907848","https://openalex.org/W2511644566","https://openalex.org/W2593378336","https://openalex.org/W2625497447","https://openalex.org/W2883603641","https://openalex.org/W2962695467"],"related_works":["https://openalex.org/W2373288511","https://openalex.org/W2990048225","https://openalex.org/W2104451027","https://openalex.org/W180059953","https://openalex.org/W1549357804","https://openalex.org/W2736779594","https://openalex.org/W2090997801","https://openalex.org/W2137189227","https://openalex.org/W2086680732","https://openalex.org/W3137054110","https://openalex.org/W2159533255","https://openalex.org/W2067125243","https://openalex.org/W3203294819","https://openalex.org/W1637974152","https://openalex.org/W3124329","https://openalex.org/W2073895427","https://openalex.org/W2059418655","https://openalex.org/W1979755623","https://openalex.org/W2884510252","https://openalex.org/W1787216088"],"abstract_inverted_index":{"Efficient":[0],"solution":[1],"of":[2,11,41,56,62,73,79,100,106,117,133],"the":[3,25,34,39,42,54,60,63,74,98,101,107,115,134],"lowest":[4],"eigenmodes":[5,61],"is":[6,22,69],"studied":[7],"for":[8],"a":[9,57,86],"family":[10],"related":[12,128],"eigenvalue":[13],"problems":[14],"with":[15,112],"common":[16],"$2\\times":[17],"2$":[18],"block":[19,28,37,48],"structure.":[20],"It":[21],"assumed":[23],"that":[24],"upper":[26],"diagonal":[27,36],"varies":[29],"between":[30],"different":[31],"versions":[32],"while":[33],"lower":[35],"and":[38],"range":[40],"coupling":[43],"blocks":[44],"remain":[45],"unchanged.":[46],"Such":[47],"structure":[49],"naturally":[50],"arises":[51],"when":[52],"studying":[53],"effect":[55],"subsystem":[58],"to":[59,95,114,129],"full":[64],"system.":[65],"The":[66],"proposed":[67],"method":[68,108],"based":[70],"on":[71],"interpolation":[72,118],"resolvent":[75],"function":[76],"after":[77],"some":[78],"its":[80],"singularities":[81],"have":[82],"been":[83],"removed":[84],"by":[85,124],"spectral":[87],"projection.":[88],"Singular":[89],"value":[90],"decomposition":[91],"can":[92],"be":[93],"used":[94],"further":[96],"reduce":[97],"dimension":[99],"computational":[102],"problem.":[103],"Error":[104],"analysis":[105],"indicates":[109],"exponential":[110],"convergence":[111],"respect":[113],"number":[116],"points.":[119],"Theoretical":[120],"results":[121],"are":[122],"illustrated":[123],"two":[125],"numerical":[126],"examples":[127],"finite":[130],"element":[131],"discretization":[132],"Laplace":[135],"operator.":[136]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}