{"id":"https://openalex.org/W3014857990","doi":"https://doi.org/10.1007/s10444-020-09787-x","title":"Structured backward error analysis for generalized saddle point problems","display_name":"Structured backward error analysis for generalized saddle point problems","publication_year":2020,"publication_date":"2020-04-01","ids":{"openalex":"https://openalex.org/W3014857990","doi":"https://doi.org/10.1007/s10444-020-09787-x","mag":"3014857990"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-020-09787-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-020-09787-x","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"Advances in Computational 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/A5062302772","display_name":"Bing Zheng","orcid":"https://orcid.org/0000-0003-0552-835X"},"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":"Bing Zheng","raw_affiliation_strings":["School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People\u2019s 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"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100677607","display_name":"Peng Lv","orcid":"https://orcid.org/0000-0001-7680-7562"},"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":"Peng Lv","raw_affiliation_strings":["School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People\u2019s 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"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5062302772"],"corresponding_institution_ids":["https://openalex.org/I76214153"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.5525,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.71771739,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"46","issue":"2","first_page":null,"last_page":null},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9993000030517578,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6867111325263977},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.6802547574043274},{"id":"https://openalex.org/keywords/kronecker-delta","display_name":"Kronecker delta","score":0.6404147148132324},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.5640485286712646},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.545596182346344},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48413071036338806},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4560295641422272},{"id":"https://openalex.org/keywords/orthographic-projection","display_name":"Orthographic projection","score":0.4327709674835205},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.4291462004184723},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.42291539907455444},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4226333498954773},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3499864935874939},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30141669511795044},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14297404885292053}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6867111325263977},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.6802547574043274},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.6404147148132324},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.5640485286712646},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.545596182346344},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48413071036338806},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4560295641422272},{"id":"https://openalex.org/C175694140","wikidata":"https://www.wikidata.org/wiki/Q980329","display_name":"Orthographic projection","level":2,"score":0.4327709674835205},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.4291462004184723},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.42291539907455444},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4226333498954773},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3499864935874939},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30141669511795044},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14297404885292053},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10444-020-09787-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-020-09787-x","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"Advances in Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/418475","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/418475","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/:262010/439424","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/439424","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":"\u671f\u520a\u8bba\u6587"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/370919","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/370919","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/:262010/431546","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/431546","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":"\u671f\u520a\u8bba\u6587"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5947849822","display_name":"\u6b63\u5219\u5316\u603b\u4f53\u6700\u5c0f\u4e8c\u4e58\u95ee\u9898\u7684\u9ad8\u6027\u80fd\u7b97\u6cd5\u53ca\u7406\u8bba\u7814\u7a76","funder_award_id":"11571004","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":37,"referenced_works":["https://openalex.org/W658559791","https://openalex.org/W1268207413","https://openalex.org/W1488435683","https://openalex.org/W1964831956","https://openalex.org/W1985050981","https://openalex.org/W1992658198","https://openalex.org/W1996259230","https://openalex.org/W1998049115","https://openalex.org/W2009452020","https://openalex.org/W2013737143","https://openalex.org/W2016127945","https://openalex.org/W2020804487","https://openalex.org/W2026927759","https://openalex.org/W2038336192","https://openalex.org/W2066668812","https://openalex.org/W2067580655","https://openalex.org/W2068193542","https://openalex.org/W2072030463","https://openalex.org/W2078696348","https://openalex.org/W2098271661","https://openalex.org/W2116208340","https://openalex.org/W2133248904","https://openalex.org/W2136722618","https://openalex.org/W2141870784","https://openalex.org/W2167491925","https://openalex.org/W2184857355","https://openalex.org/W2464196647","https://openalex.org/W2584253892","https://openalex.org/W2765671816","https://openalex.org/W2798909945","https://openalex.org/W2811099820","https://openalex.org/W2944568021","https://openalex.org/W3022136271","https://openalex.org/W3022909171","https://openalex.org/W4231405723","https://openalex.org/W4302564868","https://openalex.org/W4312258136"],"related_works":["https://openalex.org/W4236459141","https://openalex.org/W4205304778","https://openalex.org/W2020252434","https://openalex.org/W73248859","https://openalex.org/W2584253892","https://openalex.org/W2350324449","https://openalex.org/W119381072","https://openalex.org/W2034033896","https://openalex.org/W2094891943","https://openalex.org/W4240399920"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}