{"id":"https://openalex.org/W2093706117","doi":"https://doi.org/10.1080/00207169808804695","title":"Stabilization by perturbation of ILL-conditioned cyclic reduction<sup>\u2217</sup>","display_name":"Stabilization by perturbation of ILL-conditioned cyclic reduction<sup>\u2217</sup>","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2093706117","doi":"https://doi.org/10.1080/00207169808804695","mag":"2093706117"},"language":"en","primary_location":{"id":"doi:10.1080/00207169808804695","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169808804695","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer 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/A5023048493","display_name":"Velizar Pavlov","orcid":"https://orcid.org/0000-0003-1095-2470"},"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":true,"raw_author_name":"Velisar Pavlov","raw_affiliation_strings":["Center of Applied Mathematics and Informatics , University of Rousse , Rousse, 7017, Bulgaria"],"affiliations":[{"raw_affiliation_string":"Center of Applied Mathematics and Informatics , University of Rousse , Rousse, 7017, Bulgaria","institution_ids":["https://openalex.org/I4210105926"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040736315","display_name":"Plamen Y. Yalamov","orcid":null},"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":"Plamen Yalamov","raw_affiliation_strings":["Center of Applied Mathematics and Informatics , University of Rousse , Rousse, 7017, Bulgaria"],"affiliations":[{"raw_affiliation_string":"Center of Applied Mathematics and Informatics , University of Rousse , Rousse, 7017, Bulgaria","institution_ids":["https://openalex.org/I4210105926"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023048493"],"corresponding_institution_ids":["https://openalex.org/I4210105926"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.22167126,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"68","issue":"3-4","first_page":"273","last_page":"283"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9954000115394592,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9897000193595886,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.8395907878875732},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6740175485610962},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6524662971496582},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5686748027801514},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5676929950714111},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46299347281455994},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4589065611362457},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3803291320800781},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23672690987586975},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10645467042922974},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09506005048751831},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.08710211515426636}],"concepts":[{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.8395907878875732},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6740175485610962},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6524662971496582},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5686748027801514},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5676929950714111},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46299347281455994},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4589065611362457},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3803291320800781},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23672690987586975},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10645467042922974},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09506005048751831},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.08710211515426636},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169808804695","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169808804695","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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":9,"referenced_works":["https://openalex.org/W1975501665","https://openalex.org/W1978040945","https://openalex.org/W1990523337","https://openalex.org/W2006850990","https://openalex.org/W2067718978","https://openalex.org/W2119840674","https://openalex.org/W2798909945","https://openalex.org/W4241764494","https://openalex.org/W4255332333"],"related_works":["https://openalex.org/W4212973497","https://openalex.org/W1980786482","https://openalex.org/W2360550119","https://openalex.org/W3177208105","https://openalex.org/W3165035967","https://openalex.org/W2389963024","https://openalex.org/W2353849135","https://openalex.org/W1965670081","https://openalex.org/W1943105110","https://openalex.org/W2058628803"],"abstract_inverted_index":{"In":[0,71,98],"this":[1],"work":[2],"we":[3,40,66,73,88,100,127],"present":[4,128],"a":[5,18,62,75,94],"stabilization":[6],"of":[7,17,20,30,46],"the":[8,21,31,42,48,84,113,125],"Cyclic":[9],"Reduction":[10],"(CR)":[11],"for":[12,38,112],"tridiagonal":[13],"systems":[14],"which":[15,39,58,77],"consists":[16],"modification":[19],"CR":[22],"algorithm":[23,43,111],"without":[24],"back":[25],"substitution":[26],"and":[27,80],"iterative":[28,90],"improving":[29],"results.":[32,49],"We":[33],"consider":[34],"arbitrary":[35],"well-conditioned":[36],"matrices":[37],"stabilize":[41],"by":[44,56],"means":[45],"perturbing":[47],"When":[50],"it":[51],"is":[52,78,81,120],"necessary":[53],"to":[54,83,92,104],"divide":[55],"numbers":[57],"are":[59],"less":[60],"than":[61],"certain":[63],"limit":[64],"\u03b4":[65],"perturb":[67],"them":[68],"with":[69,115,134],"\u03b4.":[70],"consequence,":[72],"get":[74,105],"solution":[76],"perturbed,":[79],"close":[82],"exact":[85],"solution.":[86,97],"Then,":[87],"apply":[89],"improvement":[91],"obtain":[93],"more":[95],"accurate":[96,107],"practice":[99],"need":[101],"1-2":[102],"iterations":[103],"very":[106],"solutions.":[108],"A":[109],"fast":[110],"problem":[114],"multiple":[116],"right":[117],"hand":[118],"sides":[119],"given,":[121],"as":[122],"well.":[123],"At":[124],"end":[126],"some":[129],"numerical":[130],"evidence":[131],"including":[132],"experiments":[133],"random":[135],"matrices.":[136]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
