{"id":"https://openalex.org/W4390639736","doi":"https://doi.org/10.1080/00207160.2023.2301570","title":"Two-parameter modified matrix splitting iteration method for Helmholtz equation","display_name":"Two-parameter modified matrix splitting iteration method for Helmholtz equation","publication_year":2024,"publication_date":"2024-01-06","ids":{"openalex":"https://openalex.org/W4390639736","doi":"https://doi.org/10.1080/00207160.2023.2301570"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2023.2301570","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2023.2301570","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011404128","display_name":"T. Y. Li","orcid":null},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":false,"raw_author_name":"Tian-Yi Li","raw_affiliation_strings":["Department of Mathematics, University of Macau, Macao, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Macau, Macao, People's Republic of China","institution_ids":["https://openalex.org/I204512498"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059371977","display_name":"Fang Chen","orcid":"https://orcid.org/0000-0002-6894-5428"},"institutions":[{"id":"https://openalex.org/I78675632","display_name":"Beijing Information Science & Technology University","ror":"https://ror.org/04xnqep60","country_code":"CN","type":"education","lineage":["https://openalex.org/I78675632"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fang Chen","raw_affiliation_strings":["School of Applied Science, Beijing Information Science and Technology University, Beijing, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Applied Science, Beijing Information Science and Technology University, Beijing, People's Republic of China","institution_ids":["https://openalex.org/I78675632"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086528027","display_name":"Zhi-Wei Fang","orcid":"https://orcid.org/0000-0002-6290-0130"},"institutions":[{"id":"https://openalex.org/I14894300","display_name":"Foshan University","ror":"https://ror.org/02xvvvp28","country_code":"CN","type":"education","lineage":["https://openalex.org/I14894300"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi-Wei Fang","raw_affiliation_strings":["School of Mathematics and Big Data, Foshan University, Foshan, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Big Data, Foshan University, Foshan, People's Republic of China","institution_ids":["https://openalex.org/I14894300"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101501154","display_name":"Hai\u2010Wei Sun","orcid":"https://orcid.org/0000-0002-5507-6083"},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":true,"raw_author_name":"Hai-Wei Sun","raw_affiliation_strings":["Department of Mathematics, University of Macau, Macao, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Macau, Macao, People's Republic of China","institution_ids":["https://openalex.org/I204512498"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100376384","display_name":"Zhi Wang","orcid":"https://orcid.org/0000-0002-1095-9632"},"institutions":[{"id":"https://openalex.org/I21642278","display_name":"Ningxia University","ror":"https://ror.org/04j7b2v61","country_code":"CN","type":"education","lineage":["https://openalex.org/I21642278"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi Wang","raw_affiliation_strings":["Institute of Applied Mathematics and Mechanics, Ningxia University, Yinchuan, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics and Mechanics, Ningxia University, Yinchuan, People's Republic of China","institution_ids":["https://openalex.org/I21642278"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101501154"],"corresponding_institution_ids":["https://openalex.org/I204512498"],"apc_list":null,"apc_paid":null,"fwci":0.2882,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51683485,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"101","issue":"9-10","first_page":"1205","last_page":"1218"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.9504202604293823},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.876232385635376},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8548617362976074},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.6583911180496216},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.579306960105896},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5329588055610657},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.5263137817382812},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4933291971683502},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48736172914505005},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.47846293449401855},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45522060990333557},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43365585803985596},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.3540986478328705},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.24754321575164795},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.12081584334373474},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06679236888885498}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9504202604293823},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.876232385635376},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8548617362976074},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.6583911180496216},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.579306960105896},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5329588055610657},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.5263137817382812},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4933291971683502},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48736172914505005},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47846293449401855},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45522060990333557},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43365585803985596},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3540986478328705},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.24754321575164795},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.12081584334373474},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06679236888885498},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2023.2301570","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2023.2301570","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2313130190","display_name":null,"funder_award_id":"0122/2020/A3","funder_id":"https://openalex.org/F4320323893","funder_display_name":"Fundo para o Desenvolvimento das Ci\u00eancias e da Tecnologia"},{"id":"https://openalex.org/G2340086152","display_name":null,"funder_award_id":"12101123","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/F4320323893","display_name":"Fundo para o Desenvolvimento das Ci\u00eancias e da Tecnologia","ror":"https://ror.org/05vna4324"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W183253500","https://openalex.org/W1506342804","https://openalex.org/W1814407173","https://openalex.org/W1946675375","https://openalex.org/W1963751327","https://openalex.org/W1966763308","https://openalex.org/W1985109867","https://openalex.org/W2000065163","https://openalex.org/W2001019613","https://openalex.org/W2002102128","https://openalex.org/W2004165073","https://openalex.org/W2025124289","https://openalex.org/W2030729182","https://openalex.org/W2049726926","https://openalex.org/W2069595221","https://openalex.org/W2070875961","https://openalex.org/W2082691187","https://openalex.org/W2120704348","https://openalex.org/W2134572726","https://openalex.org/W2160910187","https://openalex.org/W2164050538","https://openalex.org/W2164639651","https://openalex.org/W2168690621","https://openalex.org/W2168999396","https://openalex.org/W2323995821","https://openalex.org/W2528120734","https://openalex.org/W2559509558","https://openalex.org/W2758237693","https://openalex.org/W2791279916","https://openalex.org/W3106831245","https://openalex.org/W3126220907","https://openalex.org/W3200756715","https://openalex.org/W4252589316","https://openalex.org/W4283641523"],"related_works":["https://openalex.org/W3157581606","https://openalex.org/W2042846224","https://openalex.org/W2113830538","https://openalex.org/W2358905935","https://openalex.org/W2942315554","https://openalex.org/W2804461272","https://openalex.org/W2382988560","https://openalex.org/W2024149451","https://openalex.org/W4322732133","https://openalex.org/W2561347830"],"abstract_inverted_index":{"For":[0],"effectively":[1],"solving":[2,91],"the":[3,11,29,59,71,76,80,92],"nonsymmetric":[4],"and":[5,36],"indefinite":[6],"linear":[7],"system":[8],"originating":[9],"from":[10],"discretized":[12],"Helmholtz":[13,93],"equation":[14,94],"with":[15],"complex":[16],"wavenumber,":[17],"we":[18],"propose":[19],"a":[20,49],"two-parameter":[21],"modified":[22],"matrix":[23],"splitting":[24],"iteration":[25,45],"method.":[26],"We":[27],"establish":[28],"asymptotic":[30],"convergence":[31,39,77],"theory":[32],"for":[33,90],"this":[34],"method":[35,46,89],"demonstrate":[37],"its":[38],"under":[40],"certain":[41],"conditions.":[42],"The":[43],"proposed":[44],"leads":[47],"to":[48,68],"new":[50,72],"preconditioner":[51,73],"that":[52,70],"can":[53],"be":[54],"efficiently":[55],"inverted":[56],"by":[57],"using":[58],"discrete":[60],"sine":[61],"transform.":[62],"Numerical":[63],"experiments":[64],"are":[65],"carried":[66],"out":[67],"show":[69],"significantly":[74],"improves":[75],"rate":[78],"of":[79,95],"GMRES":[81,88],"method,":[82],"which":[83],"results":[84],"in":[85],"effective":[86],"preconditioned":[87],"high":[96],"wavenumber.":[97]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-14T06:11:07.267592","created_date":"2025-10-10T00:00:00"}
