作者: Per Christian Hansen
DOI: 10.1007/BF01933214
关键词: Well-posed problem 、 Mathematics 、 Fourier series 、 Singular value decomposition 、 Regularization (mathematics) 、 Singular value 、 Mathematical analysis
摘要: We investigate the approximation properties of regularized solutions to discrete ill-posed least squares problems. A necessary condition for obtaining good is that Fourier coefficients right-hand side, when expressed in terms generalized SVD associated with regularization problem, on average decay zero faster than singular values. This Picard condition. illustrate importance this theoretically as well experimentally.