{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:49:59Z","timestamp":1740156599772,"version":"3.37.3"},"reference-count":13,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,12,3]],"date-time":"2013-12-03T00:00:00Z","timestamp":1386028800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11001144","ZR2012AL09"],"award-info":[{"award-number":["11001144","ZR2012AL09"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Shandong Province, China","award":["11001144","ZR2012AL09"],"award-info":[{"award-number":["11001144","ZR2012AL09"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Numerical Analysis"],"published-print":{"date-parts":[[2013,12,3]]},"abstract":"<jats:p>We present a preconditioned mixed-type splitting iterative method for solving the linear system <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>A<\/mml:mi><mml:mi>x<\/mml:mi><mml:mo>=<\/mml:mo><mml:mi>b<\/mml:mi><\/mml:math>, where <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>A<\/mml:mi><\/mml:mrow><\/mml:math> is a Z-matrix. And we give some comparison theorems to show that the rate of convergence of the preconditioned mixed-type splitting iterative method is faster than that of the mixed-type splitting iterative method. Finally, we give one numerical example to illustrate our results.<\/jats:p>","DOI":"10.1155\/2013\/512084","type":"journal-article","created":{"date-parts":[[2013,12,3]],"date-time":"2013-12-03T21:05:39Z","timestamp":1386104739000},"page":"1-7","source":"Crossref","is-referenced-by-count":0,"title":["Some Results on Preconditioned Mixed-Type Splitting Iterative Method"],"prefix":"10.1155","volume":"2013","author":[{"given":"Guangbin","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266061, China"}]},{"given":"Fuping","family":"Tan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai University, Shanghai 200444, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2007.06.033"},{"year":"1971","key":"2"},{"key":"3","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/0024-3795(84)90222-2","volume":"58","year":"1984","journal-title":"Linear Algebra and Its Applications C"},{"year":"1962","key":"4"},{"issue":"1\u20133","key":"5","first-page":"227","volume":"317","year":"2000","journal-title":"Linear Algebra and Its Applications"},{"year":"1979","key":"6a"},{"year":"1994","key":"6b"},{"year":"1994","key":"7"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.07.050"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02575836"},{"key":"10","first-page":"329","volume":"19","year":"1997","journal-title":"Bulletin of the Institute of Mathematics Academia Sinica"},{"issue":"1\u20133","key":"11","first-page":"1","volume":"282","year":"1998","journal-title":"Linear Algebra and Its Applications"},{"issue":"2","key":"12","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/S0168-9274(98)00062-2","volume":"29","year":"1999","journal-title":"Applied Numerical Mathematics"}],"container-title":["Advances in Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/archive\/2013\/512084.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/2013\/512084.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/2013\/512084.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T13:10:17Z","timestamp":1607605817000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ana\/2013\/512084\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12,3]]},"references-count":13,"alternative-id":["512084","512084"],"URL":"https:\/\/doi.org\/10.1155\/2013\/512084","relation":{},"ISSN":["1687-9562","1687-9570"],"issn-type":[{"type":"print","value":"1687-9562"},{"type":"electronic","value":"1687-9570"}],"subject":[],"published":{"date-parts":[[2013,12,3]]}}}