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It is known that iterated Tikhonov regularization often produces approximate solutions of higher quality than (standard) Tikhonov regularization. This paper discusses iterated Tikhonov regularization for large-scale problems with a general regularization matrix. Specifically, the original problem is reduced to small size by application of a fairly small number of steps of the Arnoldi or Golub-Kahan processes, and iterated Tikhonov is applied to the reduced problem. The regularization parameter is determined by using an extension of a technique first described by Donatelli and Hanke for quite special coefficient matrices. Convergence of the method is established and computed examples illustrate its performance.<\/jats:p>","DOI":"10.1007\/s11075-025-02072-2","type":"journal-article","created":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T02:01:46Z","timestamp":1746496906000},"page":"1617-1637","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Projected iterated Tikhonov in general form with adaptive choice of the regularization parameter"],"prefix":"10.1007","volume":"100","author":[{"given":"Alessandro","family":"Buccini","sequence":"first","affiliation":[]},{"given":"Silvia","family":"Gazzola","sequence":"additional","affiliation":[]},{"given":"Lucas","family":"Onisk","sequence":"additional","affiliation":[]},{"given":"Mirjeta","family":"Pasha","sequence":"additional","affiliation":[]},{"given":"Lothar","family":"Reichel","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,6]]},"reference":[{"key":"2072_CR1","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1137\/21M1441420","volume":"66","author":"J Chung","year":"2024","unstructured":"Chung, J., Gazzola, S.: Computational methods for large-scale inverse problems: a survey on hybrid projection methods. 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