{"id":"https://openalex.org/W2790005792","doi":"https://doi.org/10.1007/s11075-018-0494-2","title":"Modified PHSS iterative methods for solving nonsingular and singular saddle point problems","display_name":"Modified PHSS iterative methods for solving nonsingular and singular saddle point problems","publication_year":2018,"publication_date":"2018-02-10","ids":{"openalex":"https://openalex.org/W2790005792","doi":"https://doi.org/10.1007/s11075-018-0494-2","mag":"2790005792"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-018-0494-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-018-0494-2","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/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":true,"raw_author_name":"Zheng-Ge Huang","raw_affiliation_strings":["School of Science, Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an, 710072, Shaanxi, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Science, Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an, 710072, Shaanxi, People\u2019s Republic of China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064861169","display_name":"Ligong Wang","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":"Li-Gong Wang","raw_affiliation_strings":["School of Science, Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an, 710072, Shaanxi, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Science, Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an, 710072, Shaanxi, People\u2019s Republic of China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100440520","display_name":"Xu Zhong","orcid":"https://orcid.org/0000-0002-0619-8949"},"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":"Zhong Xu","raw_affiliation_strings":["School of Science, Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an, 710072, Shaanxi, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Science, Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an, 710072, Shaanxi, People\u2019s Republic of China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101456414","display_name":"Jingjing Cui","orcid":"https://orcid.org/0000-0002-2677-013X"},"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":"Jing-Jing Cui","raw_affiliation_strings":["School of Science, Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an, 710072, Shaanxi, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Science, Department of Applied Mathematics, Northwestern Polytechnical University, Xi\u2019an, 710072, Shaanxi, People\u2019s Republic of China","institution_ids":["https://openalex.org/I17145004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5007652836"],"corresponding_institution_ids":["https://openalex.org/I17145004"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.2137,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.52484844,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"80","issue":"2","first_page":"485","last_page":"519"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9986000061035156,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9908000230789185,"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/preconditioner","display_name":"Preconditioner","score":0.864507794380188},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.8198490142822266},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.7721226215362549},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7103856205940247},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.6800724267959595},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6082137227058411},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.594061017036438},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5872918367385864},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.5675328969955444},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47774404287338257},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46784934401512146},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.4538485109806061},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.4532455503940582},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.45267510414123535},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4516266882419586},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.41142675280570984},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2500447928905487},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2417566180229187},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.07779064774513245},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07563069462776184}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.864507794380188},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.8198490142822266},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.7721226215362549},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7103856205940247},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6800724267959595},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6082137227058411},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.594061017036438},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5872918367385864},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.5675328969955444},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47774404287338257},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46784934401512146},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.4538485109806061},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.4532455503940582},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.45267510414123535},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4516266882419586},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.41142675280570984},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2500447928905487},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2417566180229187},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07779064774513245},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07563069462776184},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-018-0494-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-018-0494-2","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/G8990637587","display_name":null,"funder_award_id":"11171273","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":42,"referenced_works":["https://openalex.org/W132749961","https://openalex.org/W1251548615","https://openalex.org/W1500921805","https://openalex.org/W1598407593","https://openalex.org/W1963751327","https://openalex.org/W1970870428","https://openalex.org/W1975719858","https://openalex.org/W1980843658","https://openalex.org/W1985340647","https://openalex.org/W1991278266","https://openalex.org/W1996107448","https://openalex.org/W2002102128","https://openalex.org/W2002852249","https://openalex.org/W2004291775","https://openalex.org/W2008893060","https://openalex.org/W2022456764","https://openalex.org/W2026635066","https://openalex.org/W2031691614","https://openalex.org/W2049157754","https://openalex.org/W2049726926","https://openalex.org/W2051686220","https://openalex.org/W2072074484","https://openalex.org/W2076495780","https://openalex.org/W2077866399","https://openalex.org/W2084740841","https://openalex.org/W2086868629","https://openalex.org/W2088456940","https://openalex.org/W2092439735","https://openalex.org/W2094290072","https://openalex.org/W2109635103","https://openalex.org/W2129625121","https://openalex.org/W2132070457","https://openalex.org/W2140153041","https://openalex.org/W2141870784","https://openalex.org/W2170040487","https://openalex.org/W2180332188","https://openalex.org/W2234276735","https://openalex.org/W2354090937","https://openalex.org/W2573068466","https://openalex.org/W3035235874","https://openalex.org/W3149667697","https://openalex.org/W4295016751"],"related_works":["https://openalex.org/W3157581606","https://openalex.org/W2113830538","https://openalex.org/W2401310550","https://openalex.org/W2385105452","https://openalex.org/W2381322109","https://openalex.org/W1189497506","https://openalex.org/W2091702533","https://openalex.org/W2034237012","https://openalex.org/W3146410598","https://openalex.org/W4287824572"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-22T08:38:42.863108","created_date":"2025-10-10T00:00:00"}
