{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T06:46:26Z","timestamp":1751870786565},"reference-count":17,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2005,7,8]],"date-time":"2005-07-08T00:00:00Z","timestamp":1120780800000},"content-version":"vor","delay-in-days":3660,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[1995,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that certain multisplitting iterative methods based on overlapping blocks yield faster convergence than corresponding nonoverlapping block iterations, provided the coefficient matrix is an M\u2010matrix. This result can be used to compare variants of the waveform relaxation algorithm for solving initial value problems. The methods under consideration use the same discretization technique, but are based on multisplittings with different overlaps. Numerical experiments on the Intel iPSC\/860 hypercube are included.<\/jats:p>","DOI":"10.1002\/nla.1680020403","type":"journal-article","created":{"date-parts":[[2005,11,1]],"date-time":"2005-11-01T19:23:16Z","timestamp":1130872996000},"page":"335-346","source":"Crossref","is-referenced-by-count":26,"title":["A comparison result for multisplittings and waveform relaxation methods"],"prefix":"10.1002","volume":"2","author":[{"given":"Andreas","family":"Frommer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bert","family":"Pohl","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2005,7,8]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(94)00194-4"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01409790"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-322-83922-0"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(89)90074-8"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02238650"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-09947-6"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1137\/0916004"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"E.Lelarasmee.The waveform relaxation method for time domain analysis of large scale nonlinear dynamical systems. Ph.D. dissertation University of California Berkeley CA 1982.","DOI":"10.1109\/TCAD.1982.1270004"},{"key":"e_1_2_1_10_2","article-title":"A note on comparison theorems on splittings and multisplittings of hermitian positive definite matrices","author":"Nabben R.","journal-title":"Linear Algebra Appl."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(87)90125-X"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01952687"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1137\/0606062"},{"key":"e_1_2_1_14_2","volume-title":"Iterative Solution of Nonlinear Equations in Several Variables","author":"Ortega J.","year":"1970"},{"key":"e_1_2_1_15_2","unstructured":"B.Pohl.Ein Algorithmus zur L\u00f6sung von Anfangswertproblemen auf Parallelrechnern. Informatik\u2010Dissertationen ETH Z\u00fcrich 37 1992."},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-9274(93)90052-S"},{"key":"e_1_2_1_17_2","volume-title":"Matrix Iterative Analysis","author":"Varga R.","year":"1962"},{"key":"e_1_2_1_18_2","volume-title":"Relaxation Techniques for the Simulation on VLSI Circuits","author":"White J.","year":"1987"}],"container-title":["Numerical Linear Algebra with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnla.1680020403","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.1680020403","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T18:40:18Z","timestamp":1698259218000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/nla.1680020403"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,7]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1995,7]]}},"alternative-id":["10.1002\/nla.1680020403"],"URL":"https:\/\/doi.org\/10.1002\/nla.1680020403","archive":["Portico"],"relation":{},"ISSN":["1070-5325","1099-1506"],"issn-type":[{"value":"1070-5325","type":"print"},{"value":"1099-1506","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,7]]}}}