{"id":"https://openalex.org/W2059559799","doi":"https://doi.org/10.1007/bf02684439","title":"Preconditioning linearized equations","display_name":"Preconditioning linearized equations","publication_year":1997,"publication_date":"1997-06-01","ids":{"openalex":"https://openalex.org/W2059559799","doi":"https://doi.org/10.1007/bf02684439","mag":"2059559799"},"language":"en","primary_location":{"id":"doi:10.1007/bf02684439","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02684439","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/A5102773573","display_name":"Eskil Hansen","orcid":"https://orcid.org/0000-0003-1187-6967"},"institutions":[{"id":"https://openalex.org/I4210156784","display_name":"Alto Neuroscience (United States)","ror":"https://ror.org/04w74e817","country_code":"US","type":"company","lineage":["https://openalex.org/I4210156784"]},{"id":"https://openalex.org/I70745867","display_name":"KLA (United States)","ror":"https://ror.org/02rqhpa98","country_code":"US","type":"company","lineage":["https://openalex.org/I70745867"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"E. R. Hansen","raw_affiliation_strings":["654 Paco Drive, 94024, Los Altos, CA, U.S.A","Los Altos, U.S.A"],"affiliations":[{"raw_affiliation_string":"654 Paco Drive, 94024, Los Altos, CA, U.S.A","institution_ids":["https://openalex.org/I70745867"]},{"raw_affiliation_string":"Los Altos, U.S.A","institution_ids":["https://openalex.org/I4210156784"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102773573"],"corresponding_institution_ids":["https://openalex.org/I4210156784","https://openalex.org/I70745867"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.19251239,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"58","issue":"2","first_page":"187","last_page":"196"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods 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/T11697","display_name":"Numerical Methods 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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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":0.8898330926895142},{"id":"https://openalex.org/keywords/precondition","display_name":"Precondition","score":0.7041505575180054},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6974233984947205},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6718144416809082},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.631388783454895},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48239433765411377},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46409836411476135},{"id":"https://openalex.org/keywords/linear-equation","display_name":"Linear equation","score":0.45217493176460266},{"id":"https://openalex.org/keywords/independent-equation","display_name":"Independent equation","score":0.4404314160346985},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.4249695837497711},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4168386161327362},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1780897080898285},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1518777310848236},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12293794751167297},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08222004771232605},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.05379045009613037}],"concepts":[{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.8898330926895142},{"id":"https://openalex.org/C192465680","wikidata":"https://www.wikidata.org/wiki/Q1413450","display_name":"Precondition","level":2,"score":0.7041505575180054},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6974233984947205},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6718144416809082},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.631388783454895},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48239433765411377},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46409836411476135},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.45217493176460266},{"id":"https://openalex.org/C200602138","wikidata":"https://www.wikidata.org/wiki/Q16979193","display_name":"Independent equation","level":3,"score":0.4404314160346985},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.4249695837497711},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4168386161327362},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1780897080898285},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1518777310848236},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12293794751167297},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08222004771232605},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.05379045009613037},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02684439","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02684439","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Climate action","score":0.4000000059604645,"id":"https://metadata.un.org/sdg/13"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W109067211","https://openalex.org/W1483874187","https://openalex.org/W1580809199","https://openalex.org/W2015902296","https://openalex.org/W2067648572","https://openalex.org/W2074068518","https://openalex.org/W2131647072","https://openalex.org/W3146520007","https://openalex.org/W4300873693"],"related_works":["https://openalex.org/W153415882","https://openalex.org/W2389121573","https://openalex.org/W4386732100","https://openalex.org/W4386770668","https://openalex.org/W960957809","https://openalex.org/W4252428448","https://openalex.org/W2480891983","https://openalex.org/W4310817948","https://openalex.org/W4309956137","https://openalex.org/W2492525511"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}