{"id":"https://openalex.org/W2003986657","doi":"https://doi.org/10.1007/s00607-007-0252-0","title":"Efficient solution of nonlinear elliptic problems using hierarchical matrices with Broyden updates","display_name":"Efficient solution of nonlinear elliptic problems using hierarchical matrices with Broyden updates","publication_year":2007,"publication_date":"2007-11-27","ids":{"openalex":"https://openalex.org/W2003986657","doi":"https://doi.org/10.1007/s00607-007-0252-0","mag":"2003986657"},"language":"en","primary_location":{"id":"doi:10.1007/s00607-007-0252-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00607-007-0252-0","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"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":"Computing","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/A5064337181","display_name":"Mario Bebendorf","orcid":null},"institutions":[{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"M. Bebendorf","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik und Informatik, Universit\u00e4t Leipzig, Johannisgasse 26, 04103, Leipzig, Germany","Universit\u00e4t Leipzig, Fakult\u00e4t f\u00fcr Mathematik und Informatik, Johannisgasse 26, 04103, Leipzig, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik und Informatik, Universit\u00e4t Leipzig, Johannisgasse 26, 04103, Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]},{"raw_affiliation_string":"Universit\u00e4t Leipzig, Fakult\u00e4t f\u00fcr Mathematik und Informatik, Johannisgasse 26, 04103, Leipzig, Germany#TAB#","institution_ids":["https://openalex.org/I926574661"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005336952","display_name":"Y. Chen","orcid":"https://orcid.org/0000-0002-0892-2697"},"institutions":[{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Y. Chen","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik und Informatik, Universit\u00e4t Leipzig, Johannisgasse 26, 04103, Leipzig, Germany","Universit\u00e4t Leipzig, Fakult\u00e4t f\u00fcr Mathematik und Informatik, Johannisgasse 26, 04103, Leipzig, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik und Informatik, Universit\u00e4t Leipzig, Johannisgasse 26, 04103, Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]},{"raw_affiliation_string":"Universit\u00e4t Leipzig, Fakult\u00e4t f\u00fcr Mathematik und Informatik, Johannisgasse 26, 04103, Leipzig, Germany#TAB#","institution_ids":["https://openalex.org/I926574661"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064337181"],"corresponding_institution_ids":["https://openalex.org/I926574661"],"apc_list":{"value":3290,"currency":"USD","value_usd":3290},"apc_paid":null,"fwci":0.3622,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.63420324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"81","issue":"4","first_page":"239","last_page":"257"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9991999864578247,"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":0.9976000189781189,"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/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.8279119729995728},{"id":"https://openalex.org/keywords/lu-decomposition","display_name":"LU decomposition","score":0.5633673667907715},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5584868788719177},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.5379005670547485},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5347897410392761},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5096793174743652},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.488988995552063},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.481341689825058},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46069997549057007},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44868505001068115},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.44415175914764404},{"id":"https://openalex.org/keywords/stiffness-matrix","display_name":"Stiffness matrix","score":0.42918357253074646},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3965616822242737},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3949958384037018},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3874218761920929},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.2820154130458832},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13125216960906982},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.09854122996330261}],"concepts":[{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.8279119729995728},{"id":"https://openalex.org/C123213974","wikidata":"https://www.wikidata.org/wiki/Q833089","display_name":"LU decomposition","level":4,"score":0.5633673667907715},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5584868788719177},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.5379005670547485},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5347897410392761},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5096793174743652},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.488988995552063},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.481341689825058},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46069997549057007},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44868505001068115},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.44415175914764404},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.42918357253074646},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3965616822242737},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3949958384037018},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3874218761920929},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.2820154130458832},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13125216960906982},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.09854122996330261},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00607-007-0252-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00607-007-0252-0","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"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":"Computing","raw_type":"journal-article"},{"id":"pmh:oai:eref.uni-bayreuth.de:8175","is_oa":false,"landing_page_url":"https://eref.uni-bayreuth.de/8175/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196442","display_name":"ERef Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Artikel in einer Zeitschrift"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W67237221","https://openalex.org/W82098087","https://openalex.org/W612879516","https://openalex.org/W1210565257","https://openalex.org/W1543500414","https://openalex.org/W1569304948","https://openalex.org/W1592141884","https://openalex.org/W1786620475","https://openalex.org/W1968376936","https://openalex.org/W1969800610","https://openalex.org/W1976986637","https://openalex.org/W1977822596","https://openalex.org/W1980455776","https://openalex.org/W1985858472","https://openalex.org/W1995590107","https://openalex.org/W2018419001","https://openalex.org/W2020804487","https://openalex.org/W2027135052","https://openalex.org/W2032842253","https://openalex.org/W2038205735","https://openalex.org/W2060449697","https://openalex.org/W2062294426","https://openalex.org/W2068484625","https://openalex.org/W2082027182","https://openalex.org/W2084835734","https://openalex.org/W2101585474","https://openalex.org/W2107501462","https://openalex.org/W2122137889","https://openalex.org/W2127001790","https://openalex.org/W2156164638","https://openalex.org/W2169384271","https://openalex.org/W2321688738","https://openalex.org/W2476550081","https://openalex.org/W4245760166","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3040723915","https://openalex.org/W2127159799","https://openalex.org/W1896162644","https://openalex.org/W1901133132","https://openalex.org/W4287724094","https://openalex.org/W2068966571","https://openalex.org/W2188650732","https://openalex.org/W1614135785","https://openalex.org/W2385824356","https://openalex.org/W2083618095"],"abstract_inverted_index":null,"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}