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  • 1
    Electronic Resource
    Electronic Resource
    Regularization,GSVD and truncatedGSVD (1989)
    Springer
    BIT 29 (1989), S. 491-504 
    Details
    ISSN: 1572-9125
    Keywords: 65F20 ; 65F30 ; Ill-posed problems ; regularization ; generalized SVD ; perturbation theory ; generalized cross-validation ; transformation to standard form
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The purpose of this paper is to analyze Tikhonov regularization in general form by means of generalized SVD (GSVD) in the same spirit as SVD is used to analyze standard-form regularization. We also define a truncated GSVD solution which is of interest in its own right and which sheds light on regularization as well. In addition, our analysis gives insight into a particular numerical method for solving the general-form problem via a transformation to standard form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02219234
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  • 2
    Electronic Resource
    Electronic Resource
    The discrete picard condition for discrete ill-posed problems (1990)
    Springer
    BIT 30 (1990), S. 658-672 
    Details
    ISSN: 1572-9125
    Keywords: 65F30 ; 65F20 ; Ill-posed problems ; Tikhonov regularization ; discrete Picard condition ; generalized SVD
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01933214
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