{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T06:00:11Z","timestamp":1759384811136},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Parallel Process. Lett."],"published-print":{"date-parts":[[2006,9]]},"abstract":"<jats:p> An earlier suggested parallel \"ring\" algorithm for solving the spatially one-dimensional initial-boundary-value problem (IBVP) for a parabolic equation using an explicit difference method is shortly described. Theoretical estimates for both of the speed-up function and the communication complexity of this parallel algorithm are studied. The speed-up function is determined as the ratio between times for realization of the algorithm in sequentional and parallel cases. Theoretical estimates of the speed-up function show the significant speed-up of the parallel algorithm in comparison with the serial one for a large number of values computed by one processor during one time level and it is shown that the the speed-up tends to the number of used processors. Communication complexity is determined as a ratio between the number of interchanges and the number of arithmetical operations. It has been proven that the coefficient of the communication complexity for spatially m-dimensional IBVP tends in general to \u00be. <\/jats:p>","DOI":"10.1142\/s0129626406002666","type":"journal-article","created":{"date-parts":[[2006,9,27]],"date-time":"2006-09-27T21:41:20Z","timestamp":1159393280000},"page":"313-321","source":"Crossref","is-referenced-by-count":7,"title":["COMMUNICATION COMPLEXITY AND SPEED-UP IN THE EXPLICIT DIFFERENCE METHOD"],"prefix":"10.1142","volume":"16","author":[{"given":"PAVOL","family":"PURCZ","sequence":"first","affiliation":[{"name":"Department of Mathematics, Technical University of Ko\u0161ice, Vysoko\u0161kolska 4, 04200 Ko\u0161ice, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-9274(93)90037-R"},{"key":"rf2","first-page":"60","volume":"43","author":"Crank J.","journal-title":"Proc. Camb. Phil. Soc."},{"key":"rf3","volume-title":"Parallel Numerical Algorithms","author":"Freeman T. L.","year":"1992"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/1032002"},{"key":"rf5","volume-title":"Matrix Computations","author":"Golub G. H.","year":"1989"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1147\/rd.182.0138"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971774"},{"key":"rf8","first-page":"36","volume":"50","author":"Purcz P.","journal-title":"Journal of Electrical Engineering"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1137\/0103003"},{"key":"rf10","first-page":"171","volume":"37","author":"Purcz P.","journal-title":"Kybernetika"},{"key":"rf11","volume-title":"Numerical Solution of Partial Differential Equation","author":"Tyrtyshnikov E. E.","year":"1992"},{"key":"rf12","first-page":"3","volume":"9","author":"Tyrtyshnikov E. E.","journal-title":"Computational Processes and Systems"},{"key":"rf13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/3-540-36607-5_13","volume":"2627","author":"Zoeteweij P.","year":"2003"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0207(19970730)40:14<2653::AID-NME180>3.0.CO;2-1"},{"key":"rf16","first-page":"43","volume":"48","author":"Pavlu\u0161 M.","journal-title":"Building Research Journal"},{"key":"rf17","unstructured":"V.\u00a0Horak and P.\u00a0Gruber, Parallel Numerics '05 (Theory and Applications) (University of Salzburg and Jozef Stefan Institute Ljubljana, 2005)\u00a0pp. 47\u201356."}],"container-title":["Parallel Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129626406002666","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T09:28:53Z","timestamp":1565170133000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129626406002666"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,9]]},"references-count":16,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2006,9]]}},"alternative-id":["10.1142\/S0129626406002666"],"URL":"https:\/\/doi.org\/10.1142\/s0129626406002666","relation":{},"ISSN":["0129-6264","1793-642X"],"issn-type":[{"value":"0129-6264","type":"print"},{"value":"1793-642X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,9]]}}}