{"id":"https://openalex.org/W2135629682","doi":"https://doi.org/10.1007/978-3-319-00410-5_10","title":"Some Properties of the Broyden Restricted Class of Updates with Oblique Projections","display_name":"Some Properties of the Broyden Restricted Class of Updates with Oblique Projections","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2135629682","doi":"https://doi.org/10.1007/978-3-319-00410-5_10","mag":"2135629682"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-319-00410-5_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-00410-5_10","pdf_url":null,"source":{"id":"https://openalex.org/S2764461748","display_name":"Studies in computational intelligence","issn_l":"1860-949X","issn":["1860-949X","1860-9503"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studies in Computational Intelligence","raw_type":"book-chapter"},"type":"book-chapter","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/A5025232474","display_name":"Andrzej Stachurski","orcid":"https://orcid.org/0000-0001-7388-9726"},"institutions":[{"id":"https://openalex.org/I108403487","display_name":"Warsaw University of Technology","ror":"https://ror.org/00y0xnp53","country_code":"PL","type":"education","lineage":["https://openalex.org/I108403487"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Andrzej Stachurski","raw_affiliation_strings":["Institute of Control and Computation Engineering, Warsaw University of Technology, Nowowiejska 15/19, 00-665, Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Control and Computation Engineering, Warsaw University of Technology, Nowowiejska 15/19, 00-665, Warsaw, Poland","institution_ids":["https://openalex.org/I108403487"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5025232474"],"corresponding_institution_ids":["https://openalex.org/I108403487"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1835443,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"169","last_page":"182"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9993000030517578,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9993000030517578,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9973000288009644,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.7888191938400269},{"id":"https://openalex.org/keywords/oblique-case","display_name":"Oblique case","score":0.7199529409408569},{"id":"https://openalex.org/keywords/oblique-projection","display_name":"Oblique projection","score":0.7138592004776001},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5014815330505371},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.4950675070285797},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.4749329686164856},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4694114625453949},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.45826536417007446},{"id":"https://openalex.org/keywords/fr\u00e9chet-derivative","display_name":"Fr\u00e9chet derivative","score":0.4543510973453522},{"id":"https://openalex.org/keywords/broyden\u2013fletcher\u2013goldfarb\u2013shanno-algorithm","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","score":0.45224320888519287},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.42421141266822815},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4130937457084656},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4082251787185669},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3794507086277008},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37046849727630615},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.21560096740722656},{"id":"https://openalex.org/keywords/orthographic-projection","display_name":"Orthographic projection","score":0.214437335729599},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19591060280799866},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16534554958343506},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1259705126285553}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7888191938400269},{"id":"https://openalex.org/C160697094","wikidata":"https://www.wikidata.org/wiki/Q1233197","display_name":"Oblique case","level":2,"score":0.7199529409408569},{"id":"https://openalex.org/C161666082","wikidata":"https://www.wikidata.org/wiki/Q14551923","display_name":"Oblique projection","level":3,"score":0.7138592004776001},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5014815330505371},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.4950675070285797},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4749329686164856},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4694114625453949},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.45826536417007446},{"id":"https://openalex.org/C118335899","wikidata":"https://www.wikidata.org/wiki/Q1305350","display_name":"Fr\u00e9chet derivative","level":3,"score":0.4543510973453522},{"id":"https://openalex.org/C132721684","wikidata":"https://www.wikidata.org/wiki/Q2877013","display_name":"Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm","level":3,"score":0.45224320888519287},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.42421141266822815},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4130937457084656},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4082251787185669},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3794507086277008},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37046849727630615},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.21560096740722656},{"id":"https://openalex.org/C175694140","wikidata":"https://www.wikidata.org/wiki/Q980329","display_name":"Orthographic projection","level":2,"score":0.214437335729599},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19591060280799866},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16534554958343506},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1259705126285553},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-319-00410-5_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-319-00410-5_10","pdf_url":null,"source":{"id":"https://openalex.org/S2764461748","display_name":"Studies in computational intelligence","issn_l":"1860-949X","issn":["1860-949X","1860-9503"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studies in Computational Intelligence","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W125509687","https://openalex.org/W613054787","https://openalex.org/W746292709","https://openalex.org/W991890457","https://openalex.org/W1507423268","https://openalex.org/W1525765095","https://openalex.org/W1597184889","https://openalex.org/W1968874483","https://openalex.org/W2002199316","https://openalex.org/W2005136695","https://openalex.org/W2018238589","https://openalex.org/W2022772618","https://openalex.org/W2032083269","https://openalex.org/W2038210983","https://openalex.org/W2042803051","https://openalex.org/W2045968916","https://openalex.org/W2077658674","https://openalex.org/W2078409719","https://openalex.org/W2103111465","https://openalex.org/W2104087272","https://openalex.org/W2110649199","https://openalex.org/W2152422232","https://openalex.org/W2161347185","https://openalex.org/W2471988522","https://openalex.org/W2611536104","https://openalex.org/W2787523326","https://openalex.org/W3000651840","https://openalex.org/W3089552053","https://openalex.org/W4212997115","https://openalex.org/W4251423481","https://openalex.org/W4285719527","https://openalex.org/W4300549156"],"related_works":["https://openalex.org/W1983117412","https://openalex.org/W2026245502","https://openalex.org/W4221162014","https://openalex.org/W1964096161","https://openalex.org/W3091576739","https://openalex.org/W2981801659","https://openalex.org/W4318192194","https://openalex.org/W4307537123","https://openalex.org/W2039312875","https://openalex.org/W2056914158"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}