{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T07:17:00Z","timestamp":1779175020437,"version":"3.51.4"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2005,8,9]],"date-time":"2005-08-09T00:00:00Z","timestamp":1123545600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2005,10]]},"DOI":"10.1007\/s00211-005-0622-5","type":"journal-article","created":{"date-parts":[[2005,8,9]],"date-time":"2005-08-09T13:39:53Z","timestamp":1123594793000},"page":"643-662","source":"Crossref","is-referenced-by-count":47,"title":["Preconditioning Landweber iteration in Hilbert scales"],"prefix":"10.1007","volume":"101","author":[{"given":"Herbert","family":"Egger","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andreas","family":"Neubauer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,8,9]]},"reference":[{"key":"622_CR1","doi-asserted-by":"crossref","unstructured":"Engl, H.W., Hanke, M., Neubauer, A.: Regularization of Inverse Problem. Kluwer Academic Publishers, 1996","DOI":"10.1007\/978-94-009-1740-8"},{"key":"622_CR2","first-page":"233","volume":"11","author":"Fridman","year":"1956","unstructured":"Fridman, V.: Methods of successive approximations for Fredholm integral equations of the first kind. Usp. Mat. Nauk 11, 233\u2013234 (1956) (in Russian)","journal-title":"Usp. Mat. Nauk"},{"key":"622_CR3","doi-asserted-by":"crossref","unstructured":"Gorenflo, R., Vesella, S.: Abel Integral Equations: Analysis and Applications. Number 1461 in Lecture Notes in Math. Springer, Berlin, 1991","DOI":"10.1007\/BFb0084665"},{"key":"622_CR4","doi-asserted-by":"crossref","unstructured":"Groetsch, C.W.: The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind. Pitman, Boston, 1984","DOI":"10.1216\/RMJ-1985-15-1-33"},{"key":"622_CR5","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01385727","volume":"60","author":"Hanke","year":"1991","unstructured":"Hanke, M.: Accelerated Landweber iterations for the solution of ill-posed equations. Numer. Math. 60, 341\u2013373 (1991)","journal-title":"Numer. Math."},{"key":"622_CR6","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s002110050158","volume":"72","author":"Hanke","year":"1995","unstructured":"Hanke, M., Neubauer, A., Scherzer, O.: A convergence analysis of the Landweber iteration for nonlinear ill-posed problems. Numer. Math. 72, 21\u201337 (1995)","journal-title":"Numer. Math."},{"key":"622_CR7","unstructured":"Hohage, T.: Iterative Methods in Inverse Obstacle Scattering: Regularization Theory of Linear and Nonlinear Exponentially Ill-Posed Problems. PhD thesis, University of Linz, 1999"},{"key":"622_CR8","unstructured":"Kaltenbacher, B., Neubauer, A., Scherzer, O.: Iterative Regularization Methods for Nonlinear Problems. 2005. (in preparation)"},{"key":"622_CR9","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1070\/RM1966v021n02ABEH004151","volume":"21","author":"Krein","year":"1966","unstructured":"Krein, S.G., Petunin, J.I.: Scales of Banach spaces. Russ. Math. Surv. 21, 85\u2013160 (1966)","journal-title":"Russ. Math. Surv."},{"key":"622_CR10","doi-asserted-by":"crossref","unstructured":"Kre\u00df, R.: Linear Integral Equations. Springer, Berlin, 1989","DOI":"10.1007\/978-3-642-97146-4"},{"key":"622_CR11","doi-asserted-by":"crossref","unstructured":"Lions, J.L., Magenes, E.: Non-Homogeneous Boundary Value Problems and Applications: Volume I. Springer, Berlin - Heidelberg, 1972","DOI":"10.1007\/978-3-642-65217-2"},{"key":"622_CR12","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1080\/00036818408839508","volume":"18","author":"Natterer","year":"1984","unstructured":"Natterer, F.: Error bounds for Tikhonov regularization in Hilbert scales. Appl. Anal. 18, 29\u201337 (1984)","journal-title":"Appl. Anal."},{"key":"622_CR13","doi-asserted-by":"crossref","unstructured":"Natterer, F.: The Mathematics of Computerized Tomography. Teubner, Stuttgart, 1986","DOI":"10.1007\/978-3-663-01409-6"},{"key":"622_CR14","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1080\/00036819208840111","volume":"46","author":"Neubauer","year":"1992","unstructured":"Neubauer, A.: Tikhonov regularization of nonlinear ill-posed problems in Hilbert scales. Appl. Anal. 46, 59\u201372 (1992)","journal-title":"Appl. Anal."},{"key":"622_CR15","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/s002110050487","volume":"85","author":"Neubauer","year":"2000","unstructured":"Neubauer, A.: On Landweber iteration for nonlinear ill-posed problems in Hilbert scales. Numer. Math. 85, 309\u2013328 (2000)","journal-title":"Numer. Math."},{"key":"622_CR16","doi-asserted-by":"crossref","first-page":"2120","DOI":"10.1137\/S0036142994269411","volume":"33","author":"Tautenhahn","year":"1996","unstructured":"Tautenhahn, U.: Error estimates for regularization methods in Hilbert scales. SIAM J. Numer. Anal. 33, 2120\u20132130 (1996)","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-005-0622-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-005-0622-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-005-0622-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,4]],"date-time":"2023-05-04T02:24:34Z","timestamp":1683167074000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-005-0622-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,8,9]]},"references-count":16,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2005,10]]}},"alternative-id":["622"],"URL":"https:\/\/doi.org\/10.1007\/s00211-005-0622-5","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,8,9]]}}}