{"id":"https://openalex.org/W2917129254","doi":"https://doi.org/10.1080/00207160.2019.1585827","title":"Modified special HSS method for discrete ill-posed problems and image restoration","display_name":"Modified special HSS method for discrete ill-posed problems and image restoration","publication_year":2019,"publication_date":"2019-02-22","ids":{"openalex":"https://openalex.org/W2917129254","doi":"https://doi.org/10.1080/00207160.2019.1585827","mag":"2917129254"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2019.1585827","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2019.1585827","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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/A5101456418","display_name":"Jingjing Cui","orcid":null},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jingjing Cui","raw_affiliation_strings":["Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xian, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xian, PR China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102210161","display_name":"Guohua Peng","orcid":null},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guohua Peng","raw_affiliation_strings":["Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xian, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xian, PR China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102204933","display_name":"Quan Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Quan Lu","raw_affiliation_strings":["Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xian, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xian, PR China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007652836","display_name":"Zhengge Huang","orcid":"https://orcid.org/0000-0003-2294-972X"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengge Huang","raw_affiliation_strings":["Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xian, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xian, PR China","institution_ids":["https://openalex.org/I17145004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101456418"],"corresponding_institution_ids":["https://openalex.org/I17145004"],"apc_list":null,"apc_paid":null,"fwci":0.6961,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.61901834,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"97","issue":"4","first_page":"739","last_page":"758"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9962000250816345,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9915000200271606,"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/mathematics","display_name":"Mathematics","score":0.7755659818649292},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.599406361579895},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5211217999458313},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.5072371959686279},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5026223659515381},{"id":"https://openalex.org/keywords/well-posed-problem","display_name":"Well-posed problem","score":0.4951561987400055},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.45684540271759033},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.45035088062286377},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.43576645851135254},{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.4189279079437256},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.41700345277786255},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4150660037994385},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3590623140335083},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3546275198459625},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.32693424820899963},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29203444719314575}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7755659818649292},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.599406361579895},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5211217999458313},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.5072371959686279},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5026223659515381},{"id":"https://openalex.org/C106214006","wikidata":"https://www.wikidata.org/wiki/Q1455898","display_name":"Well-posed problem","level":2,"score":0.4951561987400055},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.45684540271759033},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.45035088062286377},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.43576645851135254},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.4189279079437256},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.41700345277786255},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4150660037994385},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3590623140335083},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3546275198459625},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.32693424820899963},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29203444719314575},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2019.1585827","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2019.1585827","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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/G5589511122","display_name":"Lie-Poisson\u4f53\u7cfb\u4e0b\u9ad8\u632f\u8361\u95ee\u9898\u53ca\u5176\u51e0\u4f55\u79ef\u5206\u65b9\u6cd5\u7814\u7a76","funder_award_id":"10802068","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1975565380","https://openalex.org/W1990381576","https://openalex.org/W2002102128","https://openalex.org/W2005140191","https://openalex.org/W2007333267","https://openalex.org/W2024333033","https://openalex.org/W2030021140","https://openalex.org/W2030925155","https://openalex.org/W2031604650","https://openalex.org/W2033242948","https://openalex.org/W2037939967","https://openalex.org/W2053564565","https://openalex.org/W2071515371","https://openalex.org/W2140064412","https://openalex.org/W2149846618","https://openalex.org/W2163813525","https://openalex.org/W2567067827","https://openalex.org/W2757493492","https://openalex.org/W3035235874","https://openalex.org/W4246327874"],"related_works":["https://openalex.org/W4327753697","https://openalex.org/W2972080159","https://openalex.org/W2017640945","https://openalex.org/W2031473926","https://openalex.org/W2386739836","https://openalex.org/W2493083010","https://openalex.org/W2021616187","https://openalex.org/W22811207","https://openalex.org/W4308895501","https://openalex.org/W2189527329"],"abstract_inverted_index":{"For":[0],"solving":[1],"ill-posed":[2,41],"inverse":[3,42],"problems,":[4,43],"we":[5,34],"establish":[6],"a":[7,71],"modified":[8,21,37],"version":[9],"of":[10,75,89],"special":[11],"Hermitian":[12],"and":[13,44,49,79],"skew-Hermitian":[14],"splitting":[15,38],"(SHSS)":[16],"iteration":[17,53],"method,":[18],"called":[19],"the":[20,36,56,76,87,90],"SHSS":[22],"(MSHSS)":[23],"method":[24,63],"in":[25],"this":[26],"paper.":[27],"Based":[28],"on":[29],"an":[30],"augmented":[31],"system":[32],"formulation,":[33],"apply":[35],"to":[39,84],"solve":[40],"theoretically":[45],"study":[46],"its":[47,51],"convergence":[48],"determine":[50],"optimal":[52],"parameters.":[54],"Furthermore,":[55],"SOR":[57],"acceleration":[58],"scheme":[59],"for":[60],"MSHSS":[61],"iterative":[62],"is":[64],"discussed.":[65],"Finally,":[66],"numerical":[67],"experiments":[68],"arising":[69],"from":[70],"Fredholm":[72],"integral":[73],"equation":[74],"first":[77],"kind":[78],"image":[80],"restoration":[81],"are":[82],"used":[83],"further":[85],"examine":[86],"effectiveness":[88],"new":[91],"method.":[92]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
