{"id":"https://openalex.org/W3185442564","doi":"https://doi.org/10.1007/s11075-021-01142-5","title":"A two-parameter block triangular preconditioner for double saddle point problem arising from liquid crystal directors modeling","display_name":"A two-parameter block triangular preconditioner for double saddle point problem arising from liquid crystal directors modeling","publication_year":2021,"publication_date":"2021-07-23","ids":{"openalex":"https://openalex.org/W3185442564","doi":"https://doi.org/10.1007/s11075-021-01142-5","mag":"3185442564"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-021-01142-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-021-01142-5","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/A5032523768","display_name":"Jun-Li Zhu","orcid":null},"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":"Jun-Li Zhu","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":"https://orcid.org/0000-0002-0044-538X","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/A5100458038","display_name":"Yu-Jiang Wu","orcid":"https://orcid.org/0000-0002-8471-9156"},"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":"Yu-Jiang Wu","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/A5100329745","display_name":"Ai\u2010Li Yang","orcid":"https://orcid.org/0000-0002-0185-6818"},"institutions":[{"id":"https://openalex.org/I152033890","display_name":"Hainan Normal University","ror":"https://ror.org/031dhcv14","country_code":"CN","type":"education","lineage":["https://openalex.org/I152033890"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ai-Li Yang","raw_affiliation_strings":["Key Laboratory of Data Science and Intelligence Education of Ministry of Education, Hainan Normal University, Haikou, 570000, People\u2019s Republic of China","Key Laboratory of Data Science and Intelligence Education of Ministry of Education, Hainan Normal University, Haikou, 570000, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Data Science and Intelligence Education of Ministry of Education, Hainan Normal University, Haikou, 570000, People\u2019s Republic of China","institution_ids":["https://openalex.org/I152033890"]},{"raw_affiliation_string":"Key Laboratory of Data Science and Intelligence Education of Ministry of Education, Hainan Normal University, Haikou, 570000, People's Republic of China","institution_ids":["https://openalex.org/I152033890"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100329745"],"corresponding_institution_ids":["https://openalex.org/I152033890"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":1.6741,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.86382875,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"89","issue":"3","first_page":"987","last_page":"1006"},"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":0.9998000264167786,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9927999973297119,"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":0.9721792936325073},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.781079113483429},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7675312757492065},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.5670220851898193},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.5636669397354126},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5122948884963989},{"id":"https://openalex.org/keywords/triangular-matrix","display_name":"Triangular matrix","score":0.4721629321575165},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46635308861732483},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41606080532073975},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3897397816181183},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21340617537498474},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.2020091712474823},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1613936722278595},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15959039330482483},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.08641934394836426}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9721792936325073},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.781079113483429},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7675312757492065},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.5670220851898193},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.5636669397354126},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5122948884963989},{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.4721629321575165},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46635308861732483},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41606080532073975},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3897397816181183},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21340617537498474},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2020091712474823},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1613936722278595},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15959039330482483},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.08641934394836426},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11075-021-01142-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-021-01142-5","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"},{"id":"pmh:oai:/ir.lzu.edu.cn/:262010/476161","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/476161","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/452337","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/452337","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G298933424","display_name":null,"funder_award_id":"11471150","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4684678386","display_name":null,"funder_award_id":"11401281","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1516868716","https://openalex.org/W1598407593","https://openalex.org/W1970870428","https://openalex.org/W1975719858","https://openalex.org/W1991285463","https://openalex.org/W1996105227","https://openalex.org/W2002102128","https://openalex.org/W2004291775","https://openalex.org/W2026635066","https://openalex.org/W2031691614","https://openalex.org/W2036236178","https://openalex.org/W2049266129","https://openalex.org/W2056828987","https://openalex.org/W2066152591","https://openalex.org/W2077441566","https://openalex.org/W2084740841","https://openalex.org/W2092439735","https://openalex.org/W2093966594","https://openalex.org/W2130381000","https://openalex.org/W2188068098","https://openalex.org/W2412306756","https://openalex.org/W2804722640","https://openalex.org/W2841377330","https://openalex.org/W2943431470","https://openalex.org/W2948764016","https://openalex.org/W2958030328","https://openalex.org/W2973399943","https://openalex.org/W4388395150"],"related_works":["https://openalex.org/W2401310550","https://openalex.org/W2381322109","https://openalex.org/W3035142666","https://openalex.org/W2218557851","https://openalex.org/W2767153625","https://openalex.org/W1982069796","https://openalex.org/W2999046577","https://openalex.org/W1970706285","https://openalex.org/W3146410598","https://openalex.org/W3011529466"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}