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The discrete picard condition for discrete illposed problems
 Per Christian Hansen
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We investigate the approximation properties of regularized solutions to discrete illposed least squares problems. A necessary condition for obtaining good regularized solutions is that the Fourier coefficients of the righthand side, when expressed in terms of the generalized SVD associated with the regularization problem, on the average decay to zero faster than the generalized singular values. This is the discrete Picard condition. We illustrate the importance of this condition theoretically as well as experimentally.
This work was carried out during a visit to Dept. of Mathematics, UCLA, and was supported by the Danish Natural Science Foundation, by the National Science Foundation under contract NSFDMS8714612, and by the Army Research Office under contract No. DAAL0388K0085.
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 Title
 The discrete picard condition for discrete illposed problems
 Journal

BIT Numerical Mathematics
Volume 30, Issue 4 , pp 658672
 Cover Date
 19901201
 DOI
 10.1007/BF01933214
 Print ISSN
 00063835
 Online ISSN
 15729125
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 65F30
 65F20
 Illposed problems
 Tikhonov regularization
 discrete Picard condition
 generalized SVD
 Industry Sectors
 Authors

 Per Christian Hansen ^{(1)}
 Author Affiliations

 1. UNI•C, Technical University of Denmark, Building 305, DK2800, Lyngby, Denmark