An efficient method for calculating smoothing splines using orthogonal transformations

DOI10.1007/BF01390708zbMath0633.65011MaRDI QIDQ1096314

M. F. Hutchinson, Frank R. de Hoog

Publication date: 1987

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133156

zbMATH Keywords

Cholesky factorizationill-conditioningorthogonal factorizationmean squared residualpolynomial smoothing spline

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Numerical smoothing, curve fitting (65D10) Factorization of matrices (15A23) Numerical mathematical programming methods (65K05) Spline approximation (41A15) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (12)

LOWLAD: A locally weighted \(L_ 1\) smoothing spline algorithm with cross validated choice of smoothing parameters ⋮ \(M\)-type smoothing splines with auxiliary scale estimation ⋮ A Stochastic Estimator of the Trace of the Influence Matrix for Laplacian Smoothing Splines ⋮ A fast ``Monte-Carlo cross-validation procedure for large least squares problems with noisy data ⋮ Discrete mollification and automatic numerical differentiation ⋮ Accuracy and efficiency of alternative spline smoothing algorithms ⋮ Computationally efficient techniques for spatial regression with differential regularization ⋮ Source term identification in 1-D IHCP ⋮ Efficient algorithms for robust generalized cross-validation spline smoothing ⋮ A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines ⋮ Pointwise Bayesian Credible Intervals for Regularized Linear Wavelet Estimators ⋮ Numerical solution of generalized IHCP by discrete mollification

Uses Software

• CUBGCV
• IMSL Numerical Libraries

Cites Work

• Smoothing by spline functions. II
• Sur le choix du paramètre d'ajustement dans le lissage par fonctions spline
• Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation
• A practical guide to splines
• On Polya frequency functions. IV: The fundamental spline functions and their limits
• Smoothing by spline functions.
• An Algorithm for the Regularization of Ill-Conditioned, Banded Least Squares Problems
• Algorithm 642
• SPLINE FUNCTIONS AND THE PROBLEM OF GRADUATION
• Smoothing noisy data with spline functions
• Unnamed Item
• Unnamed Item

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