{"id":"https://openalex.org/W2977407579","doi":"https://doi.org/10.1515/cmam-2018-0189","title":"On the Parameter Choice in the Multilevel Augmentation Method","display_name":"On the Parameter Choice in the Multilevel Augmentation Method","publication_year":2019,"publication_date":"2019-10-01","ids":{"openalex":"https://openalex.org/W2977407579","doi":"https://doi.org/10.1515/cmam-2018-0189","mag":"2977407579"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2018-0189","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0189","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied 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/A5102217404","display_name":"Suhua Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210119042","display_name":"Gannan Normal University","ror":"https://ror.org/02jf7e446","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210119042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Suhua Yang","raw_affiliation_strings":["School of Mathematics and Computer Science , Gannan Normal University , Ganzhou 341000 , P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science , Gannan Normal University , Ganzhou 341000 , P. R. China","institution_ids":["https://openalex.org/I4210119042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109604394","display_name":"Xingjun Luo","orcid":null},"institutions":[{"id":"https://openalex.org/I4210119042","display_name":"Gannan Normal University","ror":"https://ror.org/02jf7e446","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210119042"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xingjun Luo","raw_affiliation_strings":["School of Mathematics and Computer Science , Gannan Normal University , Ganzhou 341000 , P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science , Gannan Normal University , Ganzhou 341000 , P. R. China","institution_ids":["https://openalex.org/I4210119042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100567431","display_name":"Chunmei Zeng","orcid":null},"institutions":[{"id":"https://openalex.org/I4210119042","display_name":"Gannan Normal University","ror":"https://ror.org/02jf7e446","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210119042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunmei Zeng","raw_affiliation_strings":["School of Mathematics and Computer Science , Gannan Normal University , Ganzhou 341000 , P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science , Gannan Normal University , Ganzhou 341000 , P. R. China","institution_ids":["https://openalex.org/I4210119042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100743348","display_name":"Zhihai Xu","orcid":"https://orcid.org/0000-0002-8647-2118"},"institutions":[{"id":"https://openalex.org/I4210119042","display_name":"Gannan Normal University","ror":"https://ror.org/02jf7e446","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210119042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhihai Xu","raw_affiliation_strings":["School of Mathematics and Computer Science , Gannan Normal University , Ganzhou 341000 , P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science , Gannan Normal University , Ganzhou 341000 , P. R. China","institution_ids":["https://openalex.org/I4210119042"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047727694","display_name":"Wenyu Hu","orcid":"https://orcid.org/0000-0001-5030-8423"},"institutions":[{"id":"https://openalex.org/I4210119042","display_name":"Gannan Normal University","ror":"https://ror.org/02jf7e446","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210119042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenyu Hu","raw_affiliation_strings":["School of Mathematics and Computer Science , Gannan Normal University , Ganzhou 341000 , P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science , Gannan Normal University , Ganzhou 341000 , P. R. China","institution_ids":["https://openalex.org/I4210119042"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5109604394"],"corresponding_institution_ids":["https://openalex.org/I4210119042"],"apc_list":null,"apc_paid":null,"fwci":0.3837,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.57382931,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"20","issue":"3","first_page":"555","last_page":"571"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9976999759674072,"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/T10514","display_name":"Numerical methods in engineering","score":0.994700014591217,"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/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.9511678218841553},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.8599316477775574},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.7948942184448242},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6797147989273071},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.6319862604141235},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.601324737071991},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.48743560910224915},{"id":"https://openalex.org/keywords/backus\u2013gilbert-method","display_name":"Backus\u2013Gilbert method","score":0.4684849977493286},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44282639026641846},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.41383594274520874},{"id":"https://openalex.org/keywords/regularization-perspectives-on-support-vector-machines","display_name":"Regularization perspectives on support vector machines","score":0.39900022745132446},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34370285272598267},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2550710439682007},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.21311956644058228},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05897057056427002}],"concepts":[{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.9511678218841553},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.8599316477775574},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7948942184448242},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6797147989273071},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.6319862604141235},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.601324737071991},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.48743560910224915},{"id":"https://openalex.org/C27872270","wikidata":"https://www.wikidata.org/wiki/Q4839810","display_name":"Backus\u2013Gilbert method","level":5,"score":0.4684849977493286},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44282639026641846},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.41383594274520874},{"id":"https://openalex.org/C141718189","wikidata":"https://www.wikidata.org/wiki/Q7309628","display_name":"Regularization perspectives on support vector machines","level":4,"score":0.39900022745132446},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34370285272598267},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2550710439682007},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.21311956644058228},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05897057056427002},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2018-0189","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2018-0189","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1607122493","display_name":null,"funder_award_id":"20181BAB202021","funder_id":"https://openalex.org/F4320322665","funder_display_name":"Natural Science Foundation of Jiangxi Province"},{"id":"https://openalex.org/G2089542213","display_name":null,"funder_award_id":"11361005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3314306930","display_name":null,"funder_award_id":"61863001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6556568776","display_name":null,"funder_award_id":"11661008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6991148529","display_name":null,"funder_award_id":"11761010","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8662837756","display_name":null,"funder_award_id":"61502107","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/F4320322665","display_name":"Natural Science Foundation of Jiangxi Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W114314968","https://openalex.org/W133067964","https://openalex.org/W164405121","https://openalex.org/W1570089119","https://openalex.org/W1598325079","https://openalex.org/W1980617456","https://openalex.org/W1997107933","https://openalex.org/W2008095986","https://openalex.org/W2014483478","https://openalex.org/W2017439015","https://openalex.org/W2046951210","https://openalex.org/W2047028207","https://openalex.org/W2053362821","https://openalex.org/W2059228862","https://openalex.org/W2080556621","https://openalex.org/W2157053923","https://openalex.org/W2782547861","https://openalex.org/W4243606208","https://openalex.org/W4247295697","https://openalex.org/W4321076473","https://openalex.org/W6600459194","https://openalex.org/W6602384708"],"related_works":["https://openalex.org/W2366023887","https://openalex.org/W2805921369","https://openalex.org/W2394283419","https://openalex.org/W2118199608","https://openalex.org/W2069968238","https://openalex.org/W2059130945","https://openalex.org/W2807240017","https://openalex.org/W4244092552","https://openalex.org/W2050033254","https://openalex.org/W2366469720"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"we":[4],"apply":[5],"the":[6,17,32,37,62,65],"multilevel":[7],"augmentation":[8],"method":[9,26],"for":[10,36],"solving":[11],"ill-posed":[12],"Fredholm":[13],"integral":[14],"equations":[15],"of":[16,31,42,64],"first":[18],"kind":[19],"via":[20],"iterated":[21,43],"Tikhonov":[22,44],"regularization":[23,34,45],"method.":[24,66],"The":[25,39],"leads":[27],"to":[28,60],"fast":[29],"solutions":[30],"discrete":[33],"methods":[35],"equations.":[38],"convergence":[40],"rates":[41],"are":[46,58],"achieved":[47],"by":[48],"using":[49],"a":[50],"modified":[51],"parameter":[52],"choice":[53],"strategy.":[54],"Finally,":[55],"numerical":[56],"experiments":[57],"given":[59],"illustrate":[61],"efficiency":[63]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
