caa a22 4500 465821413 CHVBK 20180323112136.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF01933214 doi (NATIONALLICENCE)springer-10.1007/BF01933214 Hansen Per UNI•C, Technical University of Denmark, Building 305, DK-2800, Lyngby, Denmark aut The discrete picard condition for discrete ill-posed problems [Elektronische Daten] [Per Hansen] 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. BIT Foundations, 1990 65F30 nationallicence 65F20 nationallicence Ill-posed problems nationallicence Tikhonov regularization nationallicence discrete Picard condition nationallicence generalized SVD nationallicence BIT Numerical Mathematics Kluwer Academic Publishers 30/4(1990-12-01), 658-672 0006-3835 30:4<658 1990 30 10543 https://doi.org/10.1007/BF01933214 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01933214 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hansen Per UNI•C, Technical University of Denmark, Building 305, DK-2800, Lyngby, Denmark aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Kluwer Academic Publishers 30/4(1990-12-01), 658-672 0006-3835 30:4<658 1990 30 10543 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer