{"id":"https://openalex.org/W1995536130","doi":"https://doi.org/10.1007/bf02684392","title":"Circulant block-factorization preconditioning of anisotropic elliptic problems","display_name":"Circulant block-factorization preconditioning of anisotropic elliptic problems","publication_year":1997,"publication_date":"1997-09-01","ids":{"openalex":"https://openalex.org/W1995536130","doi":"https://doi.org/10.1007/bf02684392","mag":"1995536130"},"language":"en","primary_location":{"id":"doi:10.1007/bf02684392","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02684392","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/A5065181102","display_name":"Ivan Lirkov","orcid":"https://orcid.org/0000-0002-5870-2588"},"institutions":[{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"I. D. Lirkov","raw_affiliation_strings":["Center for Informatics and Computer Technology, Acad. G. Bonchev str., Bl. 25-A, 1113, Sofia, Bulgaria","Center for Informatics and Computer Technology, Sofia, Bulgaria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Informatics and Computer Technology, Acad. G. Bonchev str., Bl. 25-A, 1113, Sofia, Bulgaria","institution_ids":["https://openalex.org/I4210105926"]},{"raw_affiliation_string":"Center for Informatics and Computer Technology, Sofia, Bulgaria","institution_ids":["https://openalex.org/I4210105926"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073185577","display_name":"Svetozar Margenov","orcid":"https://orcid.org/0000-0001-8858-831X"},"institutions":[{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"S. D. Margenov","raw_affiliation_strings":["Center for Informatics and Computer Technology, Acad. G. Bonchev str., Bl. 25-A, 1113, Sofia, Bulgaria","Center for Informatics and Computer Technology, Sofia, Bulgaria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Informatics and Computer Technology, Acad. G. Bonchev str., Bl. 25-A, 1113, Sofia, Bulgaria","institution_ids":["https://openalex.org/I4210105926"]},{"raw_affiliation_string":"Center for Informatics and Computer Technology, Sofia, Bulgaria","institution_ids":["https://openalex.org/I4210105926"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074536850","display_name":"Ludmil Zikatanov","orcid":"https://orcid.org/0000-0002-5189-4230"},"institutions":[{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"L. T. Zikatanov","raw_affiliation_strings":["Institute of Mathematics and Informatics, Acad. G. Bouchev str., Bl. 8, 1113, Sofia, Bulgaria","Institute of Mathematics and Informatics, Sofia, Bulgaria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Informatics, Acad. G. Bouchev str., Bl. 8, 1113, Sofia, Bulgaria","institution_ids":["https://openalex.org/I4210105926"]},{"raw_affiliation_string":"Institute of Mathematics and Informatics, Sofia, Bulgaria","institution_ids":["https://openalex.org/I4210105926"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.5548,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.8158229,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"58","issue":"3","first_page":"245","last_page":"258"},"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":0.9976000189781189,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9973999857902527,"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/circulant-matrix","display_name":"Circulant matrix","score":0.9187542200088501},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7670907974243164},{"id":"https://openalex.org/keywords/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.7042187452316284},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6323865652084351},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5960896611213684},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5690139532089233},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5005412101745605},{"id":"https://openalex.org/keywords/incomplete-cholesky-factorization","display_name":"Incomplete Cholesky factorization","score":0.4365657567977905},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4300849437713623},{"id":"https://openalex.org/keywords/incomplete-lu-factorization","display_name":"Incomplete LU factorization","score":0.42718109488487244},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.4139529764652252},{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.41382503509521484},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.41247260570526123},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38889744877815247},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.33958953619003296},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29042142629623413},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2062183916568756},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09874460101127625},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.09281617403030396}],"concepts":[{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.9187542200088501},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7670907974243164},{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.7042187452316284},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6323865652084351},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5960896611213684},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5690139532089233},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5005412101745605},{"id":"https://openalex.org/C44363057","wikidata":"https://www.wikidata.org/wiki/Q6015160","display_name":"Incomplete Cholesky factorization","level":4,"score":0.4365657567977905},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4300849437713623},{"id":"https://openalex.org/C134978465","wikidata":"https://www.wikidata.org/wiki/Q1654069","display_name":"Incomplete LU factorization","level":4,"score":0.42718109488487244},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4139529764652252},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.41382503509521484},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.41247260570526123},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38889744877815247},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.33958953619003296},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29042142629623413},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2062183916568756},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09874460101127625},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.09281617403030396},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/bf02684392","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02684392","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:CiteSeerX.psu:10.1.1.50.948","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.948","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.math.ucla.edu/pub/camreport/cam95-39.ps.gz","raw_type":"text"},{"id":"pmh:oai:bpos.bg:18014","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S7407055231","display_name":"Bulgarian Portal for Open Science","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":null,"raw_type":"journal article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W126699582","https://openalex.org/W152326368","https://openalex.org/W1493981498","https://openalex.org/W1533471646","https://openalex.org/W1557985875","https://openalex.org/W1607829564","https://openalex.org/W1968151550","https://openalex.org/W1973366577","https://openalex.org/W1975696503","https://openalex.org/W2005040897","https://openalex.org/W2027764906","https://openalex.org/W2035811094","https://openalex.org/W2039206656","https://openalex.org/W2047607068","https://openalex.org/W2048255281","https://openalex.org/W2050532615","https://openalex.org/W2063088579","https://openalex.org/W2065205300","https://openalex.org/W2079059969","https://openalex.org/W2092293277","https://openalex.org/W2134572726","https://openalex.org/W2319203890","https://openalex.org/W2497159416","https://openalex.org/W2798909945","https://openalex.org/W4232804420"],"related_works":["https://openalex.org/W2074560815","https://openalex.org/W2021639088","https://openalex.org/W2078637543","https://openalex.org/W2963052759","https://openalex.org/W2063952346","https://openalex.org/W2025836747","https://openalex.org/W2381435995","https://openalex.org/W1974421439","https://openalex.org/W1987177655","https://openalex.org/W2040807801"],"abstract_inverted_index":null,"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}