{"id":"https://openalex.org/W2090766734","doi":"https://doi.org/10.1142/s0129626406002666","title":"COMMUNICATION COMPLEXITY AND SPEED-UP IN THE EXPLICIT DIFFERENCE METHOD","display_name":"COMMUNICATION COMPLEXITY AND SPEED-UP IN THE EXPLICIT DIFFERENCE METHOD","publication_year":2006,"publication_date":"2006-09-01","ids":{"openalex":"https://openalex.org/W2090766734","doi":"https://doi.org/10.1142/s0129626406002666","mag":"2090766734"},"language":"en","primary_location":{"id":"doi:10.1142/s0129626406002666","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129626406002666","pdf_url":null,"source":{"id":"https://openalex.org/S18360026","display_name":"Parallel Processing Letters","issn_l":"0129-6264","issn":["0129-6264","1793-642X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel Processing Letters","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/A5086978913","display_name":"Pavol Purcz","orcid":"https://orcid.org/0000-0001-8609-4906"},"institutions":[{"id":"https://openalex.org/I183764125","display_name":"Technical University of Ko\u0161ice","ror":"https://ror.org/05xm08015","country_code":"SK","type":"education","lineage":["https://openalex.org/I183764125"]}],"countries":["SK"],"is_corresponding":true,"raw_author_name":"PAVOL PURCZ","raw_affiliation_strings":["Department of Mathematics, Technical University of Ko\u0161ice, Vysoko\u0161kolska 4, 04200 Ko\u0161ice, Slovakia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technical University of Ko\u0161ice, Vysoko\u0161kolska 4, 04200 Ko\u0161ice, Slovakia","institution_ids":["https://openalex.org/I183764125"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086978913"],"corresponding_institution_ids":["https://openalex.org/I183764125"],"apc_list":null,"apc_paid":null,"fwci":0.4531,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.66459008,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"16","issue":"03","first_page":"313","last_page":"321"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.993399977684021,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.993399977684021,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9871000051498413,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9847000241279602,"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/arithmetic-function","display_name":"Arithmetic function","score":0.7222409248352051},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.6161381006240845},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.600224494934082},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5838497281074524},{"id":"https://openalex.org/keywords/communication-complexity","display_name":"Communication complexity","score":0.5499781370162964},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.5095148682594299},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4917445480823517},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4435432255268097},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4204229712486267},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.3509477972984314},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.21396282315254211},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1453222632408142}],"concepts":[{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.7222409248352051},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6161381006240845},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.600224494934082},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5838497281074524},{"id":"https://openalex.org/C179145077","wikidata":"https://www.wikidata.org/wiki/Q5154130","display_name":"Communication complexity","level":2,"score":0.5499781370162964},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.5095148682594299},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4917445480823517},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4435432255268097},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4204229712486267},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.3509477972984314},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.21396282315254211},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1453222632408142},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129626406002666","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129626406002666","pdf_url":null,"source":{"id":"https://openalex.org/S18360026","display_name":"Parallel Processing Letters","issn_l":"0129-6264","issn":["0129-6264","1793-642X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel Processing Letters","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":11,"referenced_works":["https://openalex.org/W1492109951","https://openalex.org/W1890410776","https://openalex.org/W1938153123","https://openalex.org/W1970105169","https://openalex.org/W2018151913","https://openalex.org/W2074559083","https://openalex.org/W2080038255","https://openalex.org/W2095036901","https://openalex.org/W2135913665","https://openalex.org/W2186176575","https://openalex.org/W2351844501"],"related_works":["https://openalex.org/W2317245370","https://openalex.org/W4249323025","https://openalex.org/W198851386","https://openalex.org/W1980160788","https://openalex.org/W2030310580","https://openalex.org/W947442053","https://openalex.org/W2148915962","https://openalex.org/W2283866686","https://openalex.org/W27867058","https://openalex.org/W2948365806"],"abstract_inverted_index":{"An":[0],"earlier":[1],"suggested":[2],"parallel":[3,40,62,76],"\"ring\"":[4],"algorithm":[5,41,58,77],"for":[6,14,28,54,84,142],"solving":[7],"the":[8,31,35,50,57,67,71,75,81,103,104,108,121,126,136,139],"spatially":[9,143],"one-dimensional":[10],"initial-boundary-value":[11],"problem":[12],"(IBVP)":[13],"a":[15,85,118],"parabolic":[16],"equation":[17],"using":[18],"an":[19],"explicit":[20],"difference":[21],"method":[22],"is":[23,47,100,115],"shortly":[24],"described.":[25],"Theoretical":[26,64],"estimates":[27,65],"both":[29],"of":[30,38,56,66,74,88,110,123,128,138],"speed-up":[32,45,68,73,105],"function":[33,46,69],"and":[34,61,98,125],"communication":[36,140],"complexity":[37,114,141],"this":[39],"are":[42],"studied.":[43],"The":[44],"determined":[48,116],"as":[49,117],"ratio":[51,119],"between":[52,120],"times":[53],"realization":[55],"in":[59,78,147],"sequentional":[60],"cases.":[63],"show":[70],"significant":[72],"comparison":[79],"with":[80],"serial":[82],"one":[83,92,95],"large":[86],"number":[87,109,122,127],"values":[89],"computed":[90],"by":[91],"processor":[93],"during":[94],"time":[96],"level":[97],"it":[99],"shown":[101],"that":[102,135],"tends":[106,146],"to":[107,149],"used":[111],"processors.":[112],"Communication":[113],"interchanges":[124],"arithmetical":[129],"operations.":[130],"It":[131],"has":[132],"been":[133],"proven":[134],"coefficient":[137],"m-dimensional":[144],"IBVP":[145],"general":[148],"\u00be.":[150]},"counts_by_year":[{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}