The discrete picard condition of discrete ill-posed problems

作者: Per Christian Hansen

DOI: 10.1007/BF01933214

关键词: Well-posed problemMathematicsFourier seriesSingular value decompositionRegularization (mathematics)Singular valueMathematical 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.

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