BIT Numerical Mathematics

, Volume 30, Issue 4, pp 658–672

The discrete picard condition for discrete ill-posed problems

  • Per Christian Hansen
Part II Numerical Mathematics

DOI: 10.1007/BF01933214

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


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 

Copyright information

© BIT Foundations 1990

Authors and Affiliations

  • Per Christian Hansen
    • 1
  1. 1.UNI•CTechnical University of DenmarkLyngbyDenmark

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