Orthogonal splines based on \(B\)-splines -- with applications to least squares, smoothing and regularisation problems

DOI10.1007/BF02109281zbMath0798.65013MaRDI QIDQ1315179

Giuseppe Rodriguez, Sebastiano Seatzu, John C. Mason

Publication date: 17 March 1994

Published in: Numerical Algorithms (Search for Journal in Brave)

zbMATH Keywords

numerical testsleast squares approximationfinite moment problemsmoothing of noisy data\(B\)- splinesone sided orthogonal linear and cubic splinesregularisation of integral transformstwo sided orthogonal splines

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Numerical smoothing, curve fitting (65D10) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Numerical methods for integral transforms (65R10) Moment problems (44A60) Spline approximation (41A15)

Related Items (11)

Stochastic isogeometric analysis on arbitrary multipatch domains by spline dimensional decomposition ⋮ On the Cholesky factorization of the Gram matrix of locally supported functions ⋮ Dyadic diagonalization of positive definite band matrices and efficient \(B\)-spline orthogonalization ⋮ A class of \(C^2\) quasi-interpolating splines free of Gibbs phenomenon ⋮ A numerical algorithm based on modified orthogonal linear spline for solving a coupled nonlinear inverse reaction-diffusion problem ⋮ Stochastic isogeometric analysis in linear elasticity ⋮ Some properties of orthogonal linear splines and their applications to inverse problems ⋮ Ultra-Fast Approximate Inference Using Variational Functional Mixed Models ⋮ Nonparametric registration to low-dimensional function spaces ⋮ Orthogonal cubic spline basis and its applications to a partial integro-differential equation with a weakly singular kernel ⋮ A comment on the orthogonalization of B-spline basis functions and their derivatives

Cites Work

• Numerical solution of the finite moment problem in a reproducing kernel Hilbert space
• Continuous approximation methods for the regularization and smoothing of integral transforms
• Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation
• A remark on the numerical solution of linear inverse problems with discrete data
• Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy

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