{"id":"https://openalex.org/W4310611458","doi":"https://doi.org/10.3390/sym14122547","title":"A Shift-Deflation Technique for Computing a Large Quantity of Eigenpairs of the Generalized Eigenvalue Problems","display_name":"A Shift-Deflation Technique for Computing a Large Quantity of Eigenpairs of the Generalized Eigenvalue Problems","publication_year":2022,"publication_date":"2022-12-02","ids":{"openalex":"https://openalex.org/W4310611458","doi":"https://doi.org/10.3390/sym14122547"},"language":"en","primary_location":{"id":"doi:10.3390/sym14122547","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14122547","pdf_url":"https://www.mdpi.com/2073-8994/14/12/2547/pdf?version=1669964333","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/12/2547/pdf?version=1669964333","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100323700","display_name":"Wei Wei","orcid":"https://orcid.org/0000-0002-2426-3660"},"institutions":[{"id":"https://openalex.org/I167027274","display_name":"Nanjing Forestry University","ror":"https://ror.org/03m96p165","country_code":"CN","type":"education","lineage":["https://openalex.org/I167027274"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Wei","raw_affiliation_strings":["Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China","institution_ids":["https://openalex.org/I167027274"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018125731","display_name":"Xiaoping Chen","orcid":"https://orcid.org/0000-0002-3776-8211"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]},{"id":"https://openalex.org/I82760581","display_name":"Taizhou University","ror":"https://ror.org/04fzhyx73","country_code":"CN","type":"education","lineage":["https://openalex.org/I82760581"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaoping Chen","raw_affiliation_strings":["Department of Mathematics, Southeast University, Nanjing 210096, China","Department of Mathematics, Taizhou University, Taizhou 225300, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Southeast University, Nanjing 210096, China","institution_ids":["https://openalex.org/I76569877"]},{"raw_affiliation_string":"Department of Mathematics, Taizhou University, Taizhou 225300, China","institution_ids":["https://openalex.org/I82760581"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023948670","display_name":"Xueying Shi","orcid":"https://orcid.org/0000-0003-0887-491X"},"institutions":[{"id":"https://openalex.org/I82760581","display_name":"Taizhou University","ror":"https://ror.org/04fzhyx73","country_code":"CN","type":"education","lineage":["https://openalex.org/I82760581"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xueying Shi","raw_affiliation_strings":["Department of Mathematics, Taizhou University, Taizhou 225300, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Taizhou University, Taizhou 225300, China","institution_ids":["https://openalex.org/I82760581"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101958177","display_name":"An Luo","orcid":"https://orcid.org/0009-0007-8563-414X"},"institutions":[{"id":"https://openalex.org/I82760581","display_name":"Taizhou University","ror":"https://ror.org/04fzhyx73","country_code":"CN","type":"education","lineage":["https://openalex.org/I82760581"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"An Luo","raw_affiliation_strings":["Department of Mathematics, Taizhou University, Taizhou 225300, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Taizhou University, Taizhou 225300, China","institution_ids":["https://openalex.org/I82760581"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018125731"],"corresponding_institution_ids":["https://openalex.org/I76569877","https://openalex.org/I82760581"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17431658,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"12","first_page":"2547","last_page":"2547"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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":0.9991999864578247,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9979000091552734,"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8970822095870972},{"id":"https://openalex.org/keywords/deflation","display_name":"Deflation","score":0.7041571140289307},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6570079922676086},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.584862232208252},{"id":"https://openalex.org/keywords/eigenvalue-perturbation","display_name":"Eigenvalue perturbation","score":0.58433997631073},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5580454468727112},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.487323135137558},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36557281017303467},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2727055549621582},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.04910007119178772}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8970822095870972},{"id":"https://openalex.org/C8112001","wikidata":"https://www.wikidata.org/wiki/Q161081","display_name":"Deflation","level":3,"score":0.7041571140289307},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6570079922676086},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.584862232208252},{"id":"https://openalex.org/C46865736","wikidata":"https://www.wikidata.org/wiki/Q5348914","display_name":"Eigenvalue perturbation","level":3,"score":0.58433997631073},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5580454468727112},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.487323135137558},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36557281017303467},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2727055549621582},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.04910007119178772},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C126285488","wikidata":"https://www.wikidata.org/wiki/Q178476","display_name":"Monetary policy","level":2,"score":0.0},{"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/C556758197","wikidata":"https://www.wikidata.org/wiki/Q580018","display_name":"Monetary economics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14122547","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14122547","pdf_url":"https://www.mdpi.com/2073-8994/14/12/2547/pdf?version=1669964333","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:fa0c1e4e694b4177b215b48eaaca9cd2","is_oa":true,"landing_page_url":"https://doaj.org/article/fa0c1e4e694b4177b215b48eaaca9cd2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 12, p 2547 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/12/2547/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14122547","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14122547","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14122547","pdf_url":"https://www.mdpi.com/2073-8994/14/12/2547/pdf?version=1669964333","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1115266449","display_name":null,"funder_award_id":"BK20170591","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1315005627","display_name":null,"funder_award_id":"12201302","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G1506083265","display_name":null,"funder_award_id":"12001396","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G2522375178","display_name":null,"funder_award_id":"20KJB110005","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G3055065552","display_name":null,"funder_award_id":"12201302","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G3251236759","display_name":null,"funder_award_id":"21KJB110017","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4013673461","display_name":null,"funder_award_id":"12001396","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G4380663004","display_name":null,"funder_award_id":"12001396","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4812022539","display_name":null,"funder_award_id":"BK20200268","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5307292783","display_name":null,"funder_award_id":"BK20170591","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G5572383930","display_name":null,"funder_award_id":"12201302","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5933377910","display_name":null,"funder_award_id":"21KJB110017","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G6852048583","display_name":null,"funder_award_id":"BK20200268","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G7464505814","display_name":null,"funder_award_id":"2018M642130","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G7512759906","display_name":null,"funder_award_id":"BK20200268","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G7611985825","display_name":null,"funder_award_id":"20KJB110005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8139737134","display_name":null,"funder_award_id":"BK20170591","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G8336698670","display_name":null,"funder_award_id":"21KJB110017","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G8492784378","display_name":null,"funder_award_id":"2018M642130","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G8550485367","display_name":null,"funder_award_id":"20KJB110005","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G948288349","display_name":null,"funder_award_id":"2018M642130","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4310611458.pdf","grobid_xml":"https://content.openalex.org/works/W4310611458.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W207477336","https://openalex.org/W1546941425","https://openalex.org/W1963987141","https://openalex.org/W2042255949","https://openalex.org/W2056104165","https://openalex.org/W2090478366","https://openalex.org/W2147542748","https://openalex.org/W2170076210","https://openalex.org/W2576255697","https://openalex.org/W2605177467","https://openalex.org/W3006820345","https://openalex.org/W3153871697","https://openalex.org/W6608427699"],"related_works":["https://openalex.org/W2053404793","https://openalex.org/W1991902748","https://openalex.org/W2350634472","https://openalex.org/W2521304522","https://openalex.org/W1971206291","https://openalex.org/W1974991855","https://openalex.org/W2083927768","https://openalex.org/W2049790183","https://openalex.org/W2066239811","https://openalex.org/W2081248473"],"abstract_inverted_index":{"In":[0,67],"this":[1],"paper,":[2],"we":[3,40,69],"propose":[4],"a":[5,42,48],"shift-deflation":[6],"technique":[7,14],"for":[8,63],"the":[9,17,21,29,37,53,57,64,71,74,80,86,91],"generalized":[10,44,59],"eigenvalue":[11,45,60],"problems.":[12],"This":[13],"consists":[15],"of":[16,23,31,73,90],"following":[18],"two":[19],"stages:":[20],"shift":[22],"converged":[24,65],"eigenvalues":[25,55],"to":[26],"zeros,":[27],"and":[28,77,88],"deflation":[30],"these":[32],"shifted":[33],"eigenvalues.":[34],"By":[35],"performing":[36,79],"above":[38],"technique,":[39],"construct":[41],"new":[43],"problem":[46,61],"with":[47,56],"lower":[49],"dimension":[50],"which":[51],"shares":[52],"same":[54],"original":[58],"except":[62],"ones.":[66],"addition,":[68],"consider":[70],"relations":[72],"eigenvectors":[75],"before":[76],"after":[78],"technique.":[81],"Finally,":[82],"numerical":[83],"experiments":[84],"show":[85],"effectiveness":[87],"robustness":[89],"proposed":[92],"method.":[93]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}