{"id":"https://openalex.org/W2037179963","doi":"https://doi.org/10.1080/00207169908804873","title":"On the modified preconditioned simultaneous displacement (m-psd) method","display_name":"On the modified preconditioned simultaneous displacement (m-psd) method","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2037179963","doi":"https://doi.org/10.1080/00207169908804873","mag":"2037179963"},"language":"en","primary_location":{"id":"doi:10.1080/00207169908804873","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169908804873","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/A5050773996","display_name":"Da\u2010Wei Chang","orcid":"https://orcid.org/0000-0002-4317-7979"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Da-Wei Chang","raw_affiliation_strings":["Department of Mathematics , Shaanxi Normal University , Xi'an, 710062, P.R.China","Department of Mathematics, Shaanxi Normal University, Xi'an, 710062, P. R. China#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Shaanxi Normal University , Xi'an, 710062, P.R.China","institution_ids":["https://openalex.org/I88830068"]},{"raw_affiliation_string":"Department of Mathematics, Shaanxi Normal University, Xi'an, 710062, P. R. China#TAB#","institution_ids":["https://openalex.org/I88830068"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050773996"],"corresponding_institution_ids":["https://openalex.org/I88830068"],"apc_list":null,"apc_paid":null,"fwci":0.4708,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.64341567,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"4","first_page":"519","last_page":"529"},"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":0.9937000274658203,"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":0.9865000247955322,"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/mathematics","display_name":"Mathematics","score":0.839533269405365},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6821268200874329},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5506076216697693},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.5226547718048096},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5054998397827148},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49961209297180176},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.44860178232192993},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4441159665584564},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4131318926811218},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4047990143299103},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18059614300727844},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17472538352012634},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07243454456329346},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.06300568580627441}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.839533269405365},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6821268200874329},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5506076216697693},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.5226547718048096},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5054998397827148},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49961209297180176},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.44860178232192993},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4441159665584564},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4131318926811218},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4047990143299103},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18059614300727844},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17472538352012634},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07243454456329346},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.06300568580627441},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169908804873","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169908804873","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1969290389","https://openalex.org/W1980479701","https://openalex.org/W1990772930","https://openalex.org/W1995582780","https://openalex.org/W2010480715","https://openalex.org/W2020888690","https://openalex.org/W2025651316","https://openalex.org/W2035207404","https://openalex.org/W2036614499","https://openalex.org/W2071491310","https://openalex.org/W2074399137","https://openalex.org/W2087876419","https://openalex.org/W2090963365","https://openalex.org/W2114065885","https://openalex.org/W2588081979","https://openalex.org/W3035235874","https://openalex.org/W6779857112","https://openalex.org/W6982606098"],"related_works":["https://openalex.org/W2161448262","https://openalex.org/W2358921742","https://openalex.org/W2236654713","https://openalex.org/W2383395740","https://openalex.org/W2535168603","https://openalex.org/W2394000971","https://openalex.org/W1844423250","https://openalex.org/W2569456256","https://openalex.org/W2361738123","https://openalex.org/W67856596"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"derive":[4],"a":[5,14,52],"new":[6],"functional":[7],"equation":[8],"which":[9],"relates":[10],"the":[11,26,44],"eigenvalues":[12,27],"of":[13,18,28],"weakly":[15],"cyclic":[16],"matrix":[17,24,49],"index":[19],"p":[20],"block":[21],"Jacobi":[22],"iteration":[23,36],"to":[25],"its":[29],"associated":[30],"Modified":[31],"Preconditioned":[32],"Simultaneous":[33],"Displacement":[34],"(M-PSD)":[35],"matrix.":[37],"The":[38],"convergence":[39],"bound":[40],"is":[41,51],"established":[42],"for":[43],"M-PSD":[45],"method":[46],"when":[47],"coefficient":[48],"A":[50],"p-cyclic.":[53]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}