{"id":"https://openalex.org/W4309634604","doi":"https://doi.org/10.1007/s11075-022-01447-z","title":"A preconditioned general modulus-based matrix splitting iteration method for solving horizontal linear complementarity problems","display_name":"A preconditioned general modulus-based matrix splitting iteration method for solving horizontal linear complementarity problems","publication_year":2022,"publication_date":"2022-11-17","ids":{"openalex":"https://openalex.org/W4309634604","doi":"https://doi.org/10.1007/s11075-022-01447-z"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-022-01447-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-022-01447-z","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5003757399","display_name":"Si-Wei Liao","orcid":"https://orcid.org/0000-0001-5592-6597"},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Si-Wei Liao","raw_affiliation_strings":["School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People\u2019s Republic of China","School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People\u2019s Republic of China","institution_ids":["https://openalex.org/I76214153"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People's Republic of China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100693449","display_name":"Guofeng Zhang","orcid":"https://orcid.org/0000-0001-5854-5247"},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guo-Feng Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People\u2019s Republic of China","School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People\u2019s Republic of China","institution_ids":["https://openalex.org/I76214153"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People's Republic of China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029462640","display_name":"Zhao\u2010Zheng Liang","orcid":"https://orcid.org/0000-0003-3525-3051"},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhao-Zheng Liang","raw_affiliation_strings":["School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People\u2019s Republic of China","School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People\u2019s Republic of China","institution_ids":["https://openalex.org/I76214153"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People's Republic of China","institution_ids":["https://openalex.org/I76214153"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100693449"],"corresponding_institution_ids":["https://openalex.org/I76214153"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.2932,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.82416254,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"93","issue":"2","first_page":"919","last_page":"947"},"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":0.9987000226974487,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9817000031471252,"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":0.79313063621521},{"id":"https://openalex.org/keywords/matrix-splitting","display_name":"Matrix splitting","score":0.6729337573051453},{"id":"https://openalex.org/keywords/linear-complementarity-problem","display_name":"Linear complementarity problem","score":0.571561336517334},{"id":"https://openalex.org/keywords/convergent-matrix","display_name":"Convergent matrix","score":0.5535889267921448},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.5453819632530212},{"id":"https://openalex.org/keywords/modulus","display_name":"Modulus","score":0.5449097156524658},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5444846749305725},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47027140855789185},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.46642738580703735},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46359649300575256},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4520728886127472},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4392535388469696},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.43674731254577637},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3954688310623169},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.3150864839553833},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2870332598686218},{"id":"https://openalex.org/keywords/state-transition-matrix","display_name":"State-transition matrix","score":0.19836974143981934},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13231956958770752},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.08212554454803467},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06153440475463867}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.79313063621521},{"id":"https://openalex.org/C133589720","wikidata":"https://www.wikidata.org/wiki/Q6787891","display_name":"Matrix splitting","level":5,"score":0.6729337573051453},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.571561336517334},{"id":"https://openalex.org/C9848182","wikidata":"https://www.wikidata.org/wiki/Q5166397","display_name":"Convergent matrix","level":5,"score":0.5535889267921448},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.5453819632530212},{"id":"https://openalex.org/C193867417","wikidata":"https://www.wikidata.org/wiki/Q6889814","display_name":"Modulus","level":2,"score":0.5449097156524658},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5444846749305725},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47027140855789185},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.46642738580703735},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46359649300575256},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4520728886127472},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4392535388469696},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.43674731254577637},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3954688310623169},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.3150864839553833},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2870332598686218},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.19836974143981934},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13231956958770752},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.08212554454803467},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06153440475463867},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/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},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-022-01447-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-022-01447-z","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5078690391","display_name":null,"funder_award_id":"11771193","funder_id":"https://openalex.org/F4320315254","funder_display_name":"Innovative Research Group Project of the National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320315254","display_name":"Innovative Research Group Project of the National Natural Science Foundation of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1895449975","https://openalex.org/W1967497904","https://openalex.org/W1969189939","https://openalex.org/W2000151369","https://openalex.org/W2004250389","https://openalex.org/W2038265001","https://openalex.org/W2043868859","https://openalex.org/W2066563104","https://openalex.org/W2087353196","https://openalex.org/W2093993556","https://openalex.org/W2107517414","https://openalex.org/W2160211628","https://openalex.org/W2163654204","https://openalex.org/W2296233246","https://openalex.org/W2791640097","https://openalex.org/W2793531126","https://openalex.org/W2893144408","https://openalex.org/W2900674848","https://openalex.org/W2914365367","https://openalex.org/W2992218295","https://openalex.org/W3003242163","https://openalex.org/W3030990663","https://openalex.org/W3047850446","https://openalex.org/W3136534692","https://openalex.org/W4220871169","https://openalex.org/W4295016751"],"related_works":["https://openalex.org/W2352030154","https://openalex.org/W2772285241","https://openalex.org/W2981881680","https://openalex.org/W2353317030","https://openalex.org/W4225308721","https://openalex.org/W2388714848","https://openalex.org/W2005314356","https://openalex.org/W2461471765","https://openalex.org/W2050716149","https://openalex.org/W2781793179"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
