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The truncatedSVD as a method for regularization
 Per Christian Hansen
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Abstract
The truncated singular value decomposition (SVD) is considered as a method for regularization of illposed linear least squares problems. In particular, the truncated SVD solution is compared with the usual regularized solution. Necessary conditions are defined in which the two methods will yield similar results. This investigation suggests the truncated SVD as a favorable alternative to standardform regularization in cases of illconditioned matrices with welldetermined numerical rank.
This work was carried out while the author visited the Dept. of Computer Science, Stanford University, California, U.S.A., and was supported in part by National Science Foundation Grant Number DCR 8412314, by a Fulbright Supplementary Grant, and by the Danish Space Board.
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 Title
 The truncatedSVD as a method for regularization
 Journal

BIT Numerical Mathematics
Volume 27, Issue 4 , pp 534553
 Cover Date
 19871201
 DOI
 10.1007/BF01937276
 Print ISSN
 00063835
 Online ISSN
 15729125
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 65F20
 65F30
 truncated SVD
 regularization in standard form
 perturbation theory for truncated SVD
 numerical rank
 Industry Sectors
 Authors

 Per Christian Hansen ^{(1)}
 Author Affiliations

 1. Copenhagen University Observatory, Øster Voldgade 3, DK1350, København K, Denmark