The discrete picard condition for discrete ill-posed problems Part II Numerical Mathematics

Received: 15 August 1989 Revised: 15 February 1990 DOI :
10.1007/BF01933214

Cite this article as: Hansen, P.C. BIT (1990) 30: 658. doi:10.1007/BF01933214
Abstract 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.

AMS Subject classification 65F30 65F20

Key words Ill-posed problems Tikhonov regularization discrete Picard condition generalized SVD 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 NSF-DMS87-14612, and by the Army Research Office under contract No. DAAL03-88-K-0085.

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Google Scholar Authors and Affiliations 1. UNI•C Technical University of Denmark Lyngby Denmark