{"id":"https://openalex.org/W4410800538","doi":"https://doi.org/10.1587/transfun.2024eap1118","title":"A Successive Approximation Algorithm with Rayleigh Functionals for Solving Nonlinear Eigenvalue Problems","display_name":"A Successive Approximation Algorithm with Rayleigh Functionals for Solving Nonlinear Eigenvalue Problems","publication_year":2025,"publication_date":"2025-05-28","ids":{"openalex":"https://openalex.org/W4410800538","doi":"https://doi.org/10.1587/transfun.2024eap1118"},"language":"en","primary_location":{"id":"doi:10.1587/transfun.2024eap1118","is_oa":true,"landing_page_url":"https://doi.org/10.1587/transfun.2024eap1118","pdf_url":"https://www.jstage.jst.go.jp/article/transfun/advpub/0/advpub_2024EAP1118/_pdf","source":{"id":"https://openalex.org/S166990724","display_name":"IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences","issn_l":"0916-8508","issn":["0916-8508","1745-1337"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.jstage.jst.go.jp/article/transfun/advpub/0/advpub_2024EAP1118/_pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034204695","display_name":"Takafumi Miyata","orcid":"https://orcid.org/0000-0002-6829-8574"},"institutions":[{"id":"https://openalex.org/I100722782","display_name":"Fukuoka Institute of Technology","ror":"https://ror.org/00bmxak18","country_code":"JP","type":"education","lineage":["https://openalex.org/I100722782"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Takafumi MIYATA","raw_affiliation_strings":["Department of Computer Science and Engineering, Fukuoka Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Fukuoka Institute of Technology","institution_ids":["https://openalex.org/I100722782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034204695"],"corresponding_institution_ids":["https://openalex.org/I100722782"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12162387,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"E108.A","issue":"12","first_page":"1620","last_page":"1628"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.998199999332428,"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":0.998199999332428,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9940000176429749,"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"}},{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied 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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7026848793029785},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6027488708496094},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5386497974395752},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5321632623672485},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5013086795806885},{"id":"https://openalex.org/keywords/rayleigh-scattering","display_name":"Rayleigh scattering","score":0.46770569682121277},{"id":"https://openalex.org/keywords/rayleigh-quotient-iteration","display_name":"Rayleigh quotient iteration","score":0.45342564582824707},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3405873775482178},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1134328544139862},{"id":"https://openalex.org/keywords/power-iteration","display_name":"Power iteration","score":0.10791194438934326},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.07192039489746094}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7026848793029785},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6027488708496094},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5386497974395752},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5321632623672485},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5013086795806885},{"id":"https://openalex.org/C46244369","wikidata":"https://www.wikidata.org/wiki/Q193709","display_name":"Rayleigh scattering","level":2,"score":0.46770569682121277},{"id":"https://openalex.org/C117586675","wikidata":"https://www.wikidata.org/wiki/Q7298489","display_name":"Rayleigh quotient iteration","level":4,"score":0.45342564582824707},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3405873775482178},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1134328544139862},{"id":"https://openalex.org/C162443888","wikidata":"https://www.wikidata.org/wiki/Q1426504","display_name":"Power iteration","level":3,"score":0.10791194438934326},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.07192039489746094},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1587/transfun.2024eap1118","is_oa":true,"landing_page_url":"https://doi.org/10.1587/transfun.2024eap1118","pdf_url":"https://www.jstage.jst.go.jp/article/transfun/advpub/0/advpub_2024EAP1118/_pdf","source":{"id":"https://openalex.org/S166990724","display_name":"IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences","issn_l":"0916-8508","issn":["0916-8508","1745-1337"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1587/transfun.2024eap1118","is_oa":true,"landing_page_url":"https://doi.org/10.1587/transfun.2024eap1118","pdf_url":"https://www.jstage.jst.go.jp/article/transfun/advpub/0/advpub_2024EAP1118/_pdf","source":{"id":"https://openalex.org/S166990724","display_name":"IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences","issn_l":"0916-8508","issn":["0916-8508","1745-1337"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4442990971","display_name":"Fast and accurate algorithms for solving large eigenvalue problems","funder_award_id":"23K11226","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410800538.pdf","grobid_xml":"https://content.openalex.org/works/W4410800538.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W361443109","https://openalex.org/W1581306515","https://openalex.org/W2033296714","https://openalex.org/W2059710537","https://openalex.org/W2476254948","https://openalex.org/W2524731768","https://openalex.org/W3098397280","https://openalex.org/W4395081461","https://openalex.org/W6673958718","https://openalex.org/W7049378936"],"related_works":["https://openalex.org/W2140314231","https://openalex.org/W4205803876","https://openalex.org/W4297437581","https://openalex.org/W2276556578","https://openalex.org/W2014162479","https://openalex.org/W2049348317","https://openalex.org/W1976066180","https://openalex.org/W2054742348","https://openalex.org/W2088932963","https://openalex.org/W2069488105"],"abstract_inverted_index":{"This":[0,24],"paper":[1],"presents":[2],"an":[3,8,65,69],"iterative":[4],"algorithm":[5,25,36,130],"for":[6],"computing":[7],"eigenvalue":[9,22,67,84],"close":[10],"to":[11,51,56],"a":[12,20,47,116,124],"user-specified":[13],"value":[14],"and":[15,68,112,131,139],"its":[16],"corresponding":[17],"eigenvector":[18,71],"of":[19,46,72,103,126],"nonlinear":[21,54,74,105],"problem.":[23,59],"iterates":[26],"two":[27],"parts":[28],"alternately.":[29],"The":[30,78],"first":[31,88],"part":[32,80],"is":[33,49,100],"the":[34,38,43,53,57,62,73,82,87,96,101,104,109,127,132,147],"existing":[35,148],"called":[37],"successive":[39,128,149],"approximation":[40,129,150],"algorithm,":[41],"where":[42],"Taylor":[44],"expansion":[45],"matrix":[48],"used":[50],"transform":[52],"problem":[55,75],"linear":[58,63],"By":[60],"solving":[61],"problem,":[64],"approximate":[66,70,83,110,118],"are":[76],"computed.":[77],"second":[79],"refines":[81],"computed":[85],"by":[86,108],"part.":[89],"To":[90],"this":[91],"end,":[92],"we":[93],"approximately":[94],"compute":[95],"Rayleigh":[97,133],"functional,":[98],"which":[99],"solution":[102],"equation":[106],"defined":[107],"eigenvector,":[111],"use":[113],"it":[114],"as":[115],"new":[117],"eigenvalue.":[119],"Experimental":[120],"results":[121],"show":[122],"that":[123],"combination":[125],"functionals":[134],"converges":[135],"within":[136],"fewer":[137],"iterations":[138],"requires":[140],"less":[141],"computational":[142],"time":[143],"in":[144],"comparison":[145],"with":[146],"algorithms.":[151]},"counts_by_year":[],"updated_date":"2025-12-01T21:03:38.442747","created_date":"2025-10-10T00:00:00"}