Practical optimal regularization of large linear systems

Didier Girard

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1986)

  • Volume: 20, Issue: 1, page 75-87
  • ISSN: 0764-583X

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Girard, Didier. "Practical optimal regularization of large linear systems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 20.1 (1986): 75-87. <http://eudml.org/doc/193471>.

@article{Girard1986,
author = {Girard, Didier},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {regularization methods; large linear systems; noisy data; tomographical picture reconstruction problem; cross-validation method},
language = {eng},
number = {1},
pages = {75-87},
publisher = {Dunod},
title = {Practical optimal regularization of large linear systems},
url = {http://eudml.org/doc/193471},
volume = {20},
year = {1986},
}

TY - JOUR
AU - Girard, Didier
TI - Practical optimal regularization of large linear systems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1986
PB - Dunod
VL - 20
IS - 1
SP - 75
EP - 87
LA - eng
KW - regularization methods; large linear systems; noisy data; tomographical picture reconstruction problem; cross-validation method
UR - http://eudml.org/doc/193471
ER -

References

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  1. [1] C. H. REINSCH, Smoothing by spline functions II. Numer. Math., 16 (1971), pp. 451-454. Zbl1248.65020MR1553981
  2. [2] G. WAHBA, Smoothing noisy data with spline functions. Numer. Math., 24 (1975),pp. 383-393. Zbl0299.65008MR405795
  3. [3] P. WAHBA, Practical approximate solutions to linear operator équations when the data are noisy. SIAM, J. Num. Anal. 14 (1977), 651-667. Zbl0402.65032MR471299
  4. [4] P. CRAVEN, G. WAHBA, Smoothing noisy data with spline functions. Numer. Math. 31 (1979) 377-403. Zbl0377.65007MR516581
  5. [5] M. STONE, Cross-validatory choice and assessment of statistical prediction (with discussion). J. Roy. Statist. Soc, Ser. B, 36 (1974) pp. 111-147. Zbl0308.62063MR356377
  6. [6] G. GOLUB, C. REINSCH, Singular value decomposition and least square solution. Numer. Math. 14, 403-420 (1970). Zbl0181.17602MR1553974
  7. [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. [8] D. GIRARD, Les méthodes de régularisation optimale et leurs applications en tomographie. Thesis, University of Grenoble, 1984. 

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