BIT Numerical Mathematics

, Volume 30, Issue 4, pp 658–672 | Cite as

The discrete picard condition for discrete ill-posed problems

  • Per Christian Hansen
Part II Numerical Mathematics


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 


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Copyright information

© BIT Foundations 1990

Authors and Affiliations

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

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