zbMATH — the first resource for mathematics

Practical optimal regularization of large linear systems. (English) Zbl 0596.65024
The paper discusses the implementation of several regularization methods for solving large linear systems of equations in presence of noisy data. The results of simulation of a tomographical picture reconstruction problem shows that the cross-validation method is particularly efficient.
Reviewer: Petko Hr. Petkov

65F20 Numerical solutions to overdetermined systems, pseudoinverses
Full Text: DOI EuDML
[1] [1] C. H. REINSCH, Smoothing by spline functions II. Numer. Math., 16 (1971), pp. 451-454. MR1553981 · Zbl 1248.65020
[2] [2] G. WAHBA, Smoothing noisy data with spline functions. Numer. Math., 24 (1975),pp. 383-393. Zbl0299.65008 MR405795 · Zbl 0299.65008
[3] P. WAHBA, Practical approximate solutions to linear operator équations when the data are noisy. SIAM, J. Num. Anal. 14 (1977), 651-667. Zbl0402.65032 MR471299 · Zbl 0402.65032
[4] [4] P. CRAVEN, G. WAHBA, Smoothing noisy data with spline functions. Numer. Math. 31 (1979) 377-403. Zbl0377.65007 MR516581 · Zbl 0377.65007
[5] M. STONE, Cross-validatory choice and assessment of statistical prediction (with discussion). J. Roy. Statist. Soc, Ser. B, 36 (1974) pp. 111-147. Zbl0308.62063 MR356377 · Zbl 0308.62063
[6] [6] G. GOLUB, C. REINSCH, Singular value decomposition and least square solution. Numer. Math. 14, 403-420 (1970). Zbl0181.17602 MR1553974 · Zbl 0181.17602
[7] R. ALLEMAND et al., A new time-of-flight method for positron computed tomography in D. A. B. Lindberg and P. L. Reichertz Eds., Biomedical Images and Computers. Berlin : Springer, 1980.
[8] D. GIRARD, Les méthodes de régularisation optimale et leurs applications en tomographie. Thesis, University of Grenoble, 1984.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.