{"id":"https://openalex.org/W1986038455","doi":"https://doi.org/10.1090/s0025-5718-2011-02458-0","title":"Acceleration of a two-grid method for eigenvalue problems","display_name":"Acceleration of a two-grid method for eigenvalue problems","publication_year":2011,"publication_date":"2011-02-18","ids":{"openalex":"https://openalex.org/W1986038455","doi":"https://doi.org/10.1090/s0025-5718-2011-02458-0","mag":"1986038455"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2011-02458-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02458-0","pdf_url":"https://www.ams.org/mcom/2011-80-275/S0025-5718-2011-02458-0/S0025-5718-2011-02458-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2011-80-275/S0025-5718-2011-02458-0/S0025-5718-2011-02458-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029270343","display_name":"Xiaozhe Hu","orcid":"https://orcid.org/0000-0001-7533-0416"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaozhe Hu","raw_affiliation_strings":["Department of Mathematics, Zhejiang University, Yuquan Campus, Hangzhou, 310027, People\u00e2\u0080\u0099s Republic of China","Department of Mathematics , Zhejiang University, Yuquan Campus , Hangzhou, 310027, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang University, Yuquan Campus, Hangzhou, 310027, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"Department of Mathematics , Zhejiang University, Yuquan Campus , Hangzhou, 310027, People\u2019s Republic of China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074670845","display_name":"Xiaoliang Cheng","orcid":"https://orcid.org/0000-0002-3110-8052"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoliang Cheng","raw_affiliation_strings":["Department of Mathematics, Zhejiang University, Yuquan Campus, Hangzhou, 310027, People\u00e2\u0080\u0099s Republic of China","Department of Mathematics , Zhejiang University, Yuquan Campus , Hangzhou, 310027, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang University, Yuquan Campus, Hangzhou, 310027, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"Department of Mathematics , Zhejiang University, Yuquan Campus , Hangzhou, 310027, People\u2019s Republic of China","institution_ids":["https://openalex.org/I76130692"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I76130692"],"apc_list":null,"apc_paid":null,"fwci":3.4162,"has_fulltext":true,"cited_by_count":68,"citation_normalized_percentile":{"value":0.91952074,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"80","issue":"275","first_page":"1287","last_page":"1301"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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/mathematics","display_name":"Mathematics","score":0.7956483364105225},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7316109538078308},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7143594026565552},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.6977676153182983},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6328145861625671},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5167983770370483},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5091137290000916},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4985320568084717},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4953991174697876},{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.43243178725242615},{"id":"https://openalex.org/keywords/divide-and-conquer-eigenvalue-algorithm","display_name":"Divide-and-conquer eigenvalue algorithm","score":0.41854652762413025},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4067225158214569},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4052974581718445},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21584650874137878},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13032928109169006},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.07513853907585144}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7956483364105225},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7316109538078308},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7143594026565552},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.6977676153182983},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6328145861625671},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5167983770370483},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5091137290000916},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4985320568084717},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4953991174697876},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.43243178725242615},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.41854652762413025},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4067225158214569},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4052974581718445},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21584650874137878},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13032928109169006},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.07513853907585144},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-2011-02458-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02458-0","pdf_url":"https://www.ams.org/mcom/2011-80-275/S0025-5718-2011-02458-0/S0025-5718-2011-02458-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2011-02458-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02458-0","pdf_url":"https://www.ams.org/mcom/2011-80-275/S0025-5718-2011-02458-0/S0025-5718-2011-02458-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1845414935","display_name":null,"funder_award_id":"10871179","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W228399867","https://openalex.org/W1485916122","https://openalex.org/W1980455776","https://openalex.org/W1981745143","https://openalex.org/W1981792545","https://openalex.org/W1986211946","https://openalex.org/W1989343938","https://openalex.org/W2012295994","https://openalex.org/W2017786109","https://openalex.org/W2031387765","https://openalex.org/W2033653234","https://openalex.org/W2041568728","https://openalex.org/W2049460408","https://openalex.org/W2058525241","https://openalex.org/W2059586807","https://openalex.org/W2069961480","https://openalex.org/W2070441252","https://openalex.org/W2070719255","https://openalex.org/W2085422562","https://openalex.org/W2086067594","https://openalex.org/W2192056604","https://openalex.org/W2798909945","https://openalex.org/W2799267564","https://openalex.org/W4231910423","https://openalex.org/W4245403238","https://openalex.org/W6600708310","https://openalex.org/W6603036350","https://openalex.org/W6629723180"],"related_works":["https://openalex.org/W46293795","https://openalex.org/W2350895707","https://openalex.org/W2014626854","https://openalex.org/W2963566796","https://openalex.org/W2383221329","https://openalex.org/W2888762984","https://openalex.org/W2364889976","https://openalex.org/W4285722889","https://openalex.org/W2040482695","https://openalex.org/W2776155623"],"abstract_inverted_index":{"This":[0],"paper":[1,77],"provides":[2],"a":[3,24,35,52,57,63,86],"new":[4,73,108],"two-grid":[5],"discretization":[6],"method":[7],"for":[8],"solving":[9,62],"partial":[10],"differential":[11],"equation":[12,15],"or":[13],"integral":[14],"eigenvalue":[16,32,54],"problems.":[17],"In":[18],"2001,":[19],"Xu":[20],"and":[21],"Zhou":[22],"introduced":[23],"scheme":[25],"that":[26,40],"reduces":[27],"the":[28,47,69,72,80,92,104,107],"solution":[29],"of":[30,41,106],"an":[31],"problem":[33,45,55,67],"on":[34,46,56,68],"finite":[36],"element":[37],"grid":[38,49],"to":[39,90,102],"one":[42],"single":[43],"linear":[44,66],"same":[48,93],"together":[50],"with":[51],"similar":[53],"much":[58,87],"coarser":[59,88],"grid.":[60],"By":[61],"slightly":[64],"different":[65],"fine":[70],"grid,":[71],"algorithm":[74],"in":[75],"this":[76],"significantly":[78],"improves":[79],"theoretical":[81],"error":[82],"estimate":[83],"which":[84],"allows":[85],"mesh":[89],"achieve":[91],"asymptotic":[94],"convergence":[95],"rate.":[96],"Numerical":[97],"examples":[98],"are":[99],"also":[100],"provided":[101],"demonstrate":[103],"efficiency":[105],"method.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
