The discrete picard condition for discrete ill-posed problems
- Per Christian Hansen
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We investigate the approximation properties of regularized solutions to discrete ill-posed least squares problems. A necessary condition for obtaining good regularized solutions is that the Fourier coefficients of the right-hand 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.
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- The discrete picard condition for discrete ill-posed problems
BIT Numerical Mathematics
Volume 30, Issue 4 , pp 658-672
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
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- Ill-posed problems
- Tikhonov regularization
- discrete Picard condition
- generalized SVD
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- Author Affiliations
- 1. UNI•C, Technical University of Denmark, Building 305, DK-2800, Lyngby, Denmark