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Projected nonstationary iterated Tikhonov regularization

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Abstract

This paper presents a nonstationary iterated Tikhonov regularization method for the solution of large-scale Tikhonov minimization problems in general form. The method projects the large-scale problem into a sequence of generalized Krylov subspaces of low dimension. The regularization parameter is determined by the discrepancy principle. Numerical examples illustrate the effectiveness of the method.

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Acknowledgments

The authors would like to thank the referees for comments that lead to improvements of the presentation. The research of L.R. is supported in part by NSF grant DMS-1115385. The work of G.H. is supported by Fund of China Scholarship Council, the young scientic research backbone teachers of CDUT (KYGG201309). The work of F.Y. is supported by Research Fund Project (NS2014PY08) of SUSE, and Key Natural Science Foundation of Sichuan Education Department (15ZA0234).

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Correspondence to Lothar Reichel.

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Communicated by Zhong-Zhi Bai.

Dedicated to Heinrich Voss on the occasion of his 70th birthday.

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Huang, G., Reichel, L. & Yin, F. Projected nonstationary iterated Tikhonov regularization. Bit Numer Math 56, 467–487 (2016). https://doi.org/10.1007/s10543-015-0568-7

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