{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T09:27:57Z","timestamp":1789723677610,"version":"4.0.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,7,1]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>\nA multilevel augmentation method is considered to solve parameter identification problems in elliptic systems. With the help of the natural linearization technique, the identification problems can be\ntransformed into a linear ill-posed operation equation, where noise\nexists not only in RHS data but also in operators. Based on multiscale decomposition in solution space, the multilevel augmentation method leads to a fast algorithm for solving discretized ill-posed problems.\nCombining with Tikhonov regularization, in the implementation of the multilevel augmentation method, one only needs to invert\nthe same matrix with a relatively small size and perform a matrix-vector multiplication at the linear computational complexity. As a result, the\ncomputation cost is dramatically reduced. The a\u00a0posteriori regularization\nparameter choice rule and the convergence rate for the regularized\nsolution are also studied in this work. Numerical tests illustrate the proposed algorithm and the theoretical estimates.\n<\/jats:p>","DOI":"10.1515\/cmam-2013-0009","type":"journal-article","created":{"date-parts":[[2013,9,27]],"date-time":"2013-09-27T16:01:19Z","timestamp":1380297679000},"page":"349-362","source":"Crossref","is-referenced-by-count":3,"title":["A Fast Algorithm for Parameter Identification Problems Based on the Multilevel Augmentation Method"],"prefix":"10.1515","volume":"13","author":[{"given":"Hui","family":"Cao","sequence":"first","affiliation":[{"name":"1School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, P.\u00a0R.\u00a0China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M. Thamban","family":"Nair","sequence":"additional","affiliation":[{"name":"2Department of Mathematics, IIT Madras, Chennai 600036, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/13\/3\/article-p349.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/downloadpdf\/journals\/cmam\/13\/3\/article-p349.xml","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T03:03:42Z","timestamp":1614481422000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2013-0009\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,7,1]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.1515\/cmam-2013-0009","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,7,1]]}}}