{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,28]],"date-time":"2024-05-28T11:07:33Z","timestamp":1716894453758},"reference-count":20,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>We present a new iterative method which does not involve inversion of the operators for obtaining an approximate solution for the nonlinear ill-posed operator equation<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>F<\/mml:mi><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><mml:mo>=<\/mml:mo><mml:mi>y<\/mml:mi><\/mml:mrow><\/mml:math>. The proposed method is a modified form of Tikhonov gradient (TIGRA) method considered by Ramlau (2003). The regularization parameter is chosen according to the balancing principle considered by Pereverzev and Schock (2005). The error estimate is derived under a general source condition and is of optimal order. Some numerical examples involving integral equations are also given in this paper.<\/jats:p>","DOI":"10.1155\/2014\/754154","type":"journal-article","created":{"date-parts":[[2014,4,18]],"date-time":"2014-04-18T01:27:25Z","timestamp":1397784445000},"page":"1-8","source":"Crossref","is-referenced-by-count":6,"title":["Inverse Free Iterative Methods for Nonlinear Ill-Posed Operator Equations"],"prefix":"10.1155","volume":"2014","author":[{"given":"Ioannis K.","family":"Argyros","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Santhosh","family":"George","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575025, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Jidesh","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575025, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"8","year":"1996"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050442"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/19\/1\/301"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/5\/4\/007"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/5\/4\/008"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/19\/2\/312"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050158"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1080\/01630569908816882"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/13\/1\/007"},{"issue":"9","key":"6","first-page":"1353","volume":"32","year":"1992","journal-title":"Computational Mathematics and Mathematical Physics"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/17.3.421"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1080\/01630569708816804"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1515\/JIIP.2010.004"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/13\/3\/012"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1080\/01630569608816691"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142903433819"},{"key":"1","year":"2008"},{"issue":"4","key":"22","doi-asserted-by":"crossref","first-page":"444","DOI":"10.2478\/cmam-2010-0026","volume":"10","year":"2010","journal-title":"Computational Methods in Applied Mathematics"},{"issue":"11","key":"24","first-page":"58","volume":"32","year":"1996","journal-title":"Izvestiya, Physics of the Solid Earth"},{"issue":"2","key":"25","first-page":"85","volume":"19","year":"2013","journal-title":"Proceedings in Mathematics and Machanics"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2014\/754154.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2014\/754154.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2014\/754154.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,18]],"date-time":"2020-08-18T00:42:34Z","timestamp":1597711354000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2014\/754154\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":20,"alternative-id":["754154","754154"],"URL":"https:\/\/doi.org\/10.1155\/2014\/754154","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}