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A Fortran package for generalized, cross-validatory spline smoothing and differentiation

1986; Elsevier BV; Volume: 8; Issue: 2 Linguagem: Inglês

10.1016/0141-1195(86)90098-7

1878-3066

Herman J. Woltring,

Advanced Optimization Algorithms Research

Based on the spline software of Lyche et al., a subroutine package is presented in which the amount of smoothing on a set of n noisy datapoints is determined from the data by means of the Generalized Cross-Validation (GCV) or predicted Mean-Squared Error (MSE) criteria of Wahba and her collaborators. Following an idea of Hutchinson and de Hoog, an efficient O (m2n) algorithm is used for calculating the criterion functions, where 2m is the order of the spline function. In this fashion, earlier O (n3) approaches based on the singular value decomposition can be avoided.