Journal
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
Volume 31, Issue 3, Pages 918-941Publisher
SIAM PUBLICATIONS
DOI: 10.1137/070709086
Keywords
ill-posed problems; inverse problems; noisy right-hand side; noisy operator; regularized total least squares; multi-parameter regularization; error bounds
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For solving linear ill-posed problems, regularization methods are required when the right-hand side and/or the operator are corrupted by some noise. In the present paper, regularized solutions are constructed using regularized total least squares (RTLS) and dual regularized total least squares (DRTLS). We discuss computational aspects and provide order optimal error bounds that characterize the accuracy of the regularized solutions. The results extend earlier results where the operator is exactly given. We also present some numerical experiments, which shed light on the relationship between RTLS, DRTLS, and the standard Tikhonov regularization.
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