{"id":"https://openalex.org/W1976239022","doi":"https://doi.org/10.1080/10637190412331279975","title":"A Distributed Normalized Explicit Preconditioned Conjugate Gradient Method","display_name":"A Distributed Normalized Explicit Preconditioned Conjugate Gradient Method","publication_year":2004,"publication_date":"2004-06-01","ids":{"openalex":"https://openalex.org/W1976239022","doi":"https://doi.org/10.1080/10637190412331279975","mag":"1976239022"},"language":"en","primary_location":{"id":"doi:10.1080/10637190412331279975","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10637190412331279975","pdf_url":null,"source":{"id":"https://openalex.org/S89732838","display_name":"Parallel algorithms and applications","issn_l":"1026-7689","issn":["1026-7689","1029-032X","1063-7192"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel Algorithms and Applications","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/A5004595458","display_name":"George A. Gravvanis","orcid":"https://orcid.org/0000-0003-1562-3633"},"institutions":[{"id":"https://openalex.org/I231025917","display_name":"Hellenic Open University","ror":"https://ror.org/02kq26x23","country_code":"GR","type":"education","lineage":["https://openalex.org/I231025917"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"G.A. Gravvanis","raw_affiliation_strings":["Department of Computer Science , Hellenic Open University , Patras, Greece","Department of Computer Science, Hellenic Open University, Patras, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science , Hellenic Open University , Patras, Greece","institution_ids":["https://openalex.org/I231025917"]},{"raw_affiliation_string":"Department of Computer Science, Hellenic Open University, Patras, Greece","institution_ids":["https://openalex.org/I231025917"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062155072","display_name":"Konstantinos M. Giannoutakis","orcid":"https://orcid.org/0000-0001-8939-4912"},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"K.M. Giannoutakis","raw_affiliation_strings":["Department of Informatics and Telecommunications , University of Athens , Panepistimioupolis, GR, 157 84, Athens, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Informatics and Telecommunications , University of Athens , Panepistimioupolis, GR, 157 84, Athens, Greece","institution_ids":["https://openalex.org/I200777214"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030989334","display_name":"Nikolaos M. Missirlis","orcid":"https://orcid.org/0000-0002-9707-7324"},"institutions":[{"id":"https://openalex.org/I200777214","display_name":"National and Kapodistrian University of Athens","ror":"https://ror.org/04gnjpq42","country_code":"GR","type":"education","lineage":["https://openalex.org/I200777214"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"N.M. Missirlis \u2020","raw_affiliation_strings":["Department of Informatics and Telecommunications , University of Athens , Panepistimioupolis, GR, 157 84, Athens, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Informatics and Telecommunications , University of Athens , Panepistimioupolis, GR, 157 84, Athens, Greece","institution_ids":["https://openalex.org/I200777214"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5004595458"],"corresponding_institution_ids":["https://openalex.org/I231025917"],"apc_list":null,"apc_paid":null,"fwci":1.0115,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.75011353,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"2-3","first_page":"163","last_page":"174"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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":0.9976999759674072,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9714999794960022,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.8847526907920837},{"id":"https://openalex.org/keywords/mimd","display_name":"MIMD","score":0.761107861995697},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6825487017631531},{"id":"https://openalex.org/keywords/distributed-memory","display_name":"Distributed memory","score":0.5678963661193848},{"id":"https://openalex.org/keywords/message-passing-interface","display_name":"Message Passing Interface","score":0.5455266833305359},{"id":"https://openalex.org/keywords/biconjugate-gradient-method","display_name":"Biconjugate gradient method","score":0.5432840585708618},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.5196115374565125},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.49387866258621216},{"id":"https://openalex.org/keywords/biconjugate-gradient-stabilized-method","display_name":"Biconjugate gradient stabilized method","score":0.4597189426422119},{"id":"https://openalex.org/keywords/interface","display_name":"Interface (matter)","score":0.45171549916267395},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.4433179795742035},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4432699680328369},{"id":"https://openalex.org/keywords/derivation-of-the-conjugate-gradient-method","display_name":"Derivation of the conjugate gradient method","score":0.4390296936035156},{"id":"https://openalex.org/keywords/conjugate","display_name":"Conjugate","score":0.4355706572532654},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43203556537628174},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4315369427204132},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.41361570358276367},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38844358921051025},{"id":"https://openalex.org/keywords/shared-memory","display_name":"Shared memory","score":0.29050788283348083},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2791910767555237},{"id":"https://openalex.org/keywords/message-passing","display_name":"Message passing","score":0.2778471112251282},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.21845585107803345},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15512734651565552},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12955138087272644},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07657822966575623}],"concepts":[{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.8847526907920837},{"id":"https://openalex.org/C21032095","wikidata":"https://www.wikidata.org/wiki/Q1149237","display_name":"MIMD","level":2,"score":0.761107861995697},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6825487017631531},{"id":"https://openalex.org/C91481028","wikidata":"https://www.wikidata.org/wiki/Q1054686","display_name":"Distributed memory","level":3,"score":0.5678963661193848},{"id":"https://openalex.org/C166782233","wikidata":"https://www.wikidata.org/wiki/Q127879","display_name":"Message Passing Interface","level":3,"score":0.5455266833305359},{"id":"https://openalex.org/C89408827","wikidata":"https://www.wikidata.org/wiki/Q855169","display_name":"Biconjugate gradient method","level":5,"score":0.5432840585708618},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.5196115374565125},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.49387866258621216},{"id":"https://openalex.org/C120553275","wikidata":"https://www.wikidata.org/wiki/Q4903720","display_name":"Biconjugate gradient stabilized method","level":3,"score":0.4597189426422119},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.45171549916267395},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.4433179795742035},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4432699680328369},{"id":"https://openalex.org/C198562538","wikidata":"https://www.wikidata.org/wiki/Q5262612","display_name":"Derivation of the conjugate gradient method","level":5,"score":0.4390296936035156},{"id":"https://openalex.org/C197336794","wikidata":"https://www.wikidata.org/wiki/Q5161150","display_name":"Conjugate","level":2,"score":0.4355706572532654},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43203556537628174},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4315369427204132},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.41361570358276367},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38844358921051025},{"id":"https://openalex.org/C133875982","wikidata":"https://www.wikidata.org/wiki/Q764810","display_name":"Shared memory","level":2,"score":0.29050788283348083},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2791910767555237},{"id":"https://openalex.org/C854659","wikidata":"https://www.wikidata.org/wiki/Q1859284","display_name":"Message passing","level":2,"score":0.2778471112251282},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.21845585107803345},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15512734651565552},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12955138087272644},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07657822966575623},{"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/C129307140","wikidata":"https://www.wikidata.org/wiki/Q6795880","display_name":"Maximum bubble pressure method","level":3,"score":0.0},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C157915830","wikidata":"https://www.wikidata.org/wiki/Q2928001","display_name":"Bubble","level":2,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10637190412331279975","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10637190412331279975","pdf_url":null,"source":{"id":"https://openalex.org/S89732838","display_name":"Parallel algorithms and applications","issn_l":"1026-7689","issn":["1026-7689","1029-032X","1063-7192"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel Algorithms and Applications","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":19,"referenced_works":["https://openalex.org/W1507319095","https://openalex.org/W1531886005","https://openalex.org/W1546004968","https://openalex.org/W1552224009","https://openalex.org/W1966704369","https://openalex.org/W1981220107","https://openalex.org/W1982064072","https://openalex.org/W1982980519","https://openalex.org/W1997210084","https://openalex.org/W2006637940","https://openalex.org/W2038516134","https://openalex.org/W2058273413","https://openalex.org/W2064211634","https://openalex.org/W2087233357","https://openalex.org/W2089099677","https://openalex.org/W2132536544","https://openalex.org/W2154851099","https://openalex.org/W2914876264","https://openalex.org/W3022841918"],"related_works":["https://openalex.org/W2073922269","https://openalex.org/W1848849174","https://openalex.org/W177599668","https://openalex.org/W4362580740","https://openalex.org/W3010456047","https://openalex.org/W2118010673","https://openalex.org/W2984664785","https://openalex.org/W2129625121","https://openalex.org/W2279364295","https://openalex.org/W2744145798"],"abstract_inverted_index":{"A":[0],"new":[1],"parallel":[2],"normalized":[3,12],"explicit":[4],"preconditioned":[5],"conjugate":[6],"gradient":[7],"method":[8,32],"in":[9],"conjunction":[10],"with":[11],"approximate":[13],"inverse":[14],"matrix":[15],"techniques":[16],"is":[17,40,62],"presented":[18],"for":[19],"solving":[20],"efficiently":[21],"sparse":[22],"linear":[23],"systems":[24],"on":[25,33,51],"multi-computer":[26],"systems.":[27],"Application":[28],"of":[29],"the":[30],"proposed":[31],"a":[34,52],"three":[35],"dimensional":[36],"boundary":[37],"value":[38],"problem":[39],"discussed":[41],"and":[42,49],"numerical":[43],"results":[44],"are":[45],"given.":[46],"The":[47],"implementation":[48],"performance":[50],"distributed,":[53],"memory":[54],"MIMD":[55],"machine,":[56],"using":[57],"message":[58],"passing":[59],"interface":[60],"(MPI)":[61],"also":[63],"investigated.":[64]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
