{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,4]],"date-time":"2024-03-04T09:21:40Z","timestamp":1709544100707},"reference-count":8,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"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":[[2013]]},"abstract":"<jats:p>Diagonal updating scheme is among the cheapest Newton-like methods for solving system of nonlinear equations. Nevertheless, the method has some shortcomings. In this paper, we proposed an improved matrix-free secant updating scheme via line search strategies, by using the steps of backtracking in the Armijo-type line search as a step length predictor and Wolfe-Like condition as corrector. Our approach aims at improving the overall performance of diagonal secant updating scheme. Under mild assumptions, the global convergence results have been presented. Numerical experiments verify that the proposed approach is very promising.<\/jats:p>","DOI":"10.1155\/2013\/814587","type":"journal-article","created":{"date-parts":[[2013,2,19]],"date-time":"2013-02-19T23:00:04Z","timestamp":1361314804000},"page":"1-6","source":"Crossref","is-referenced-by-count":2,"title":["An Enhanced Matrix-Free Secant Method via Predictor-Corrector Modified Line Search Strategies for Solving Systems of Nonlinear Equations"],"prefix":"10.1155","volume":"2013","author":[{"given":"M. Y.","family":"Waziri","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia"},{"name":"Department of Mathematical Sciences, Faculty of Science, Bayero University Kano, Kano, Nigeria"}]},{"given":"Z. A.","family":"Majid","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia"},{"name":"Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia"}]}],"member":"98","reference":[{"key":"1","year":"1983"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.3844\/jmssp.2010.246.252"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/348654"},{"key":"2","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1090\/S0025-5718-1965-0198670-6","volume":"19","year":"1965","journal-title":"Mathematics of Computation"},{"key":"8","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1090\/S0025-5718-01-01322-9","volume":"71","year":"2001","journal-title":"Mathematics of Computation"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970944"},{"issue":"1","key":"4","first-page":"59","volume":"6","year":"2012","journal-title":"Malaysian Journal of Mathematical Sciences"},{"key":"6","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1016\/0009-2509(80)85088-3","volume":"35","year":"1980","journal-title":"Chemical Engineering Sceinces"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/814587.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/814587.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/814587.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T07:50:15Z","timestamp":1498031415000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2013\/814587\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":8,"alternative-id":["814587","814587"],"URL":"https:\/\/doi.org\/10.1155\/2013\/814587","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}