{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,26]],"date-time":"2026-04-26T09:17:13Z","timestamp":1777195033861,"version":"3.51.4"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1999,3,1]],"date-time":"1999-03-01T00:00:00Z","timestamp":920246400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[1999,3,1]],"date-time":"1999-03-01T00:00:00Z","timestamp":920246400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Algorithms"],"published-print":{"date-parts":[[1999,3]]},"DOI":"10.1023\/a:1019139414435","type":"journal-article","created":{"date-parts":[[2003,2,19]],"date-time":"2003-02-19T23:30:27Z","timestamp":1045697427000},"page":"1-22","source":"Crossref","is-referenced-by-count":10,"title":["The conjugate gradient method for linear ill-posed problems with operator perturbations"],"prefix":"10.1007","volume":"20","author":[{"given":"Robert","family":"Plato","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"329294_CR1","doi-asserted-by":"crossref","first-page":"835","DOI":"10.1088\/0266-5611\/14\/4\/005","volume":"14","author":"G. Bruckner","year":"1998","unstructured":"G. Bruckner, S. Handrock-Meyer and H. Langmach, An inverse problem from 2D-groundwater modelling, Inverse Problems 14 (1998) 835\u2013851.","journal-title":"Inverse Problems"},{"key":"329294_CR2","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/BF01385614","volume":"58","author":"B. Eicke","year":"1990","unstructured":"B. Eicke, A.K. Louis and R. Plato, The instability of some gradient methods for ill-posed problems, Numer. Math. 58 (1990) 129\u2013134.","journal-title":"Numer. Math."},{"key":"329294_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-1740-8","volume-title":"Regularization of Inverse Problems","author":"H.W. Engl","year":"1996","unstructured":"H.W. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems, 1st ed. (Kluwer, Dordrecht, 1996).","edition":"1st ed."},{"key":"329294_CR4","volume-title":"Approximate Solution of Ill-Posed Problems","author":"S.F. Gilyazov","year":"1995","unstructured":"S.F. Gilyazov, Approximate Solution of Ill-Posed Problems, 1st ed. (Publisher Moscow University, Moscow, 1995) (in Russian).","edition":"1st ed."},{"key":"329294_CR5","first-page":"385","volume":"35","author":"S.F. Gilyazov","year":"1995","unstructured":"S.F. Gilyazov, Regularizing conjugate-direction methods, Comput. Math. Math. Phys. 35 (1995) 385\u2013394.","journal-title":"Comput. Math. Math. Phys."},{"key":"329294_CR6","volume-title":"Conjugate Gradient Type Methods for Ill-Posed Problems","author":"M. Hanke","year":"1995","unstructured":"M. Hanke, Conjugate Gradient Type Methods for Ill-Posed Problems, 1st ed. (Longman, Harlow, 1995).","edition":"1st ed."},{"key":"329294_CR7","doi-asserted-by":"crossref","first-page":"3487","DOI":"10.1090\/S0002-9939-1995-1285994-5","volume":"123","author":"M. Hanke","year":"1995","unstructured":"M. Hanke, The minimal error method is a regularization method, Proc. Amer. Math. Soc. 123 (1995) 3487\u20133497.","journal-title":"Proc. Amer. Math. Soc."},{"key":"329294_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-5338-9","volume-title":"An Introduction to the Mathematical Theory of Inverse Problems","author":"A. Kirsch","year":"1996","unstructured":"A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems, 1st ed. (Springer, New York, 1996).","edition":"1st ed."},{"key":"329294_CR9","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/0041-5553(86)90002-9","volume":"26","author":"A.S. Nemirovskii","year":"1986","unstructured":"A.S. Nemirovskii, The regularizing properties of the adjoint gradient method in ill-posed problems, U.S.S.R. Comput. Math. Math. Phys. 26 (1986) 7\u201316.","journal-title":"U.S.S.R. Comput. Math. Math. Phys."},{"key":"329294_CR10","first-page":"1","volume":"22","author":"A.S. Nemirovskii","year":"1984","unstructured":"A.S. Nemirovskii and B.T. Polyak, Iterative methods for solving linear ill-posed problems under precise information I, Moscow Univ. Comput. Math. Cybernet. 22 (1984) 1\u201311.","journal-title":"Moscow Univ. Comput. Math. Cybernet."},{"key":"329294_CR11","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1080\/01630569008816364","volume":"11","author":"R. Plato","year":"1990","unstructured":"R. Plato, Optimal algorithms for linear ill-posed problems yield regularization methods, Numer. Funct. Anal. Optim. 11 (1990) 111\u2013118.","journal-title":"Numer. Funct. Anal. Optim."},{"key":"329294_CR12","doi-asserted-by":"crossref","first-page":"1621","DOI":"10.1137\/S0036142997317924","volume":"35","author":"R. Plato","year":"1998","unstructured":"R. Plato, The method of conjugate residuals for solving the Galerkin equations associated with symmetric positive semidefinite ill-posed problems, SIAM J. Numer. Anal. 35 (1998) 1621\u20131645.","journal-title":"SIAM J. Numer. Anal."},{"key":"329294_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-5592-3","volume-title":"Introduction to Numerical Analysis","author":"J. Stoer","year":"1980","unstructured":"J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 1st ed. (Springer, New York, 1980).","edition":"1st ed."},{"key":"329294_CR14","volume-title":"Introduction to Functional Analysis","author":"A.E. Taylor","year":"1980","unstructured":"A.E. Taylor and D. Lay, Introduction to Functional Analysis, 2nd ed. (Wiley, New York, 1980).","edition":"2nd ed."},{"key":"329294_CR15","first-page":"451","volume-title":"Proc. of the Conf. on Finite Element Methods, 50 Years of the Courant Element","author":"E. Vainikko","year":"1993","unstructured":"E. Vainikko, Courant elements for the inverse problem in the filtration coefficient identification, in: Proc. of the Conf. on Finite Element Methods, 50 Years of the Courant Element, Univ. Jyv\u00e4skyl\u00e4, Finland (1993), eds. M. Krizek et al. (Marcel Dekker, New York, ) pp. 451\u2013459."},{"key":"329294_CR16","first-page":"202","volume-title":"Proc. of the Conf. on Ill-Posed Problems in Natural Sciences","author":"G. Vainikko","year":"1991","unstructured":"G. Vainikko, Identification of filtration coefficient in an elliptic boundary problem, in: Proc. of the Conf. on Ill-Posed Problems in Natural Sciences, Moscow, 1991, ed. A.N. Tikhonov (VSP, Utrecht,) pp. 202\u2013213."},{"key":"329294_CR17","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1080\/01630569208816485","volume":"13","author":"G. Vainikko","year":"1992","unstructured":"G. Vainikko, On the discretization and regularization of ill-posed problems with noncompact operators, Numer. Funct. Anal. Optim. 13 (1992) 381\u2013396.","journal-title":"Numer. Funct. Anal. Optim."},{"key":"329294_CR18","doi-asserted-by":"crossref","first-page":"327","DOI":"10.4171\/zaa\/562","volume":"12","author":"G. Vainikko","year":"1993","unstructured":"G. Vainikko and K. Kunisch, Identifiability of the transmissitivity coefficient in an elliptic boundary value problem, Z. Anal. Anwendungen 12 (1993) 327\u2013341.","journal-title":"Z. Anal. Anwendungen"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1019139414435.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1019139414435\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1019139414435.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T06:38:43Z","timestamp":1751870323000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1019139414435"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,3]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1999,3]]}},"alternative-id":["329294"],"URL":"https:\/\/doi.org\/10.1023\/a:1019139414435","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,3]]}}}