{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T21:01:15Z","timestamp":1648674075126},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2013,6]]},"abstract":"<jats:p> In this paper, we use matrix multisplitting with weighting parameters as the preconditioner of A. The optimal weighting parameters are determined by the approaching theory, and the scale of approaching is defined by F-norm, 2-norm, and \u221e-norm, respectively. Base on these three minimize models, three algorithms are presented and the convergence theories are established. Finally, numerical examples show that the preconditioner with the optimal weighting parameters, which are obtained from minimize F-norm and 2-norm models, can improve the condition number of A effectively. Besides, general weighting parameters are more effective than non-negative weighting parameters. <\/jats:p>","DOI":"10.1142\/s0217595913400071","type":"journal-article","created":{"date-parts":[[2013,6,27]],"date-time":"2013-06-27T02:06:26Z","timestamp":1372298786000},"page":"1340007","source":"Crossref","is-referenced-by-count":0,"title":["THREE OPTIMIZATION MODELS FOR MULTISPLITTING PRECONDITIONER"],"prefix":"10.1142","volume":"30","author":[{"given":"LIANG","family":"WEI","sequence":"first","affiliation":[{"name":"Institution of Mathematics, Taiyuan University of Technology, Taiyuan 030024, Shanxi Province, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CHUAN-LONG","family":"WANG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Taiyuan Normal University, Taiyuan 030012, Shanxi Province, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,6,26]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01934996"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511624100"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2002.7176"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599356900"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827594271421"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595294691"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(98)00118-4"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598339372"},{"key":"rf9","volume-title":"Introduction to Minimax","author":"Demyanov V. F.","year":"1974"},{"key":"rf10","volume-title":"Special Matrix Analysis and Application","author":"Huang T.-Z.","year":"2007"},{"key":"rf11","volume-title":"Algorithm and Theorem for Numerical Optimization","author":"Li D.-H.","year":"2010"},{"key":"rf12","volume-title":"Numerical Analysis","author":"Li Q.-Y.","year":"2008"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2008.10.096"},{"key":"rf14","volume-title":"Optimization Theorem and Method","author":"Yuan Y.-X.","year":"1997"},{"key":"rf15","volume-title":"Matrix Analysis and Application","author":"Zhou J.","year":"2008"}],"container-title":["Asia-Pacific Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0217595913400071","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:32:51Z","timestamp":1565116371000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0217595913400071"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6]]},"references-count":15,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2013,6,26]]},"published-print":{"date-parts":[[2013,6]]}},"alternative-id":["10.1142\/S0217595913400071"],"URL":"https:\/\/doi.org\/10.1142\/s0217595913400071","relation":{},"ISSN":["0217-5959","1793-7019"],"issn-type":[{"value":"0217-5959","type":"print"},{"value":"1793-7019","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,6]]}}}