Regularization parameter determination for discrete ill-posed problems

M.E. Hochstenbach, L. Reichel, G. Rodriguez

Research output: Contribution to journalArticleAcademicpeer-review

30 Citations (Scopus)
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Abstract

The straightforward solution of discrete ill-posed linear systems of equations or least-squares problems with error contaminated data does not, in general, give meaningful results, because the propagated error destroys the computed solution. The problems have to be modified to reduce their sensitivity to the error in the data. The amount of modification is determined by a regularization parameter. It can be difficult to determine a suitable value of the regularization parameter when no knowledge of the norm of error in the data is available. This paper proposes a new simple technique for determining a value of the regularization parameter that can be applied in this situation. It is based on comparing computed solutions determined by Tikhonov regularization and truncated singular value decomposition. Analogous comparisons are proposed for large-scale problems. The technique for determining the regularization parameter implicity provides an estimate for the norm of the error in the data. Keywords: Ill-posed problem; Regularization; Noise level estimation; TSVD; Tikhonov regularization; Heuristic parameter choice rule
Original languageEnglish
Pages (from-to)132-149
Number of pages18
JournalJournal of Computational and Applied Mathematics
Volume273
Issue number1
DOIs
Publication statusPublished - 2015

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