Multilevel regularization of wavelet based fitting of scattered data -- some experiments

DOI10.1007/s11075-004-3622-0zbMath1069.65012OpenAlexW1966859766MaRDI QIDQ1776170

Daniel Castaño, Angela Kunoth

Publication date: 20 May 2005

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

Full work available at URL: https://doi.org/10.1007/s11075-004-3622-0

zbMATH Keywords

waveletsregularizationnumerical examplesscattered datafractional Sobolev normsleast squares approximationgeophysical datafitting algorithmfitting surfacegeneralized multilevel cross-validation

Mathematics Subject Classification ID

Numerical smoothing, curve fitting (65D10) Nonparametric statistical resampling methods (62G09) Numerical methods for wavelets (65T60) Geodesy, mapping problems (86A30)

Related Items

Spherical harmonics for surface parametrisation and remeshing, A proximal-based algorithm for piecewise sparse approximation with application to scattered data fitting, \(L_1C^1\) polynomial spline approximation algorithms for large data sets, Inverse-free recursive multiresolution algorithms for a data approximation problem, Polyharmonic splines: an approximation method for noisy scattered data of extra-large size, Fast iterative solution of elliptic control problems in wavelet discretization, Scattered data reconstruction by regularization in B-spline and associated wavelet spaces

Uses Software

• mctoolbox
• FITPACK

Cites Work

• Preconditioners for least squares problems by LU factorization
• Adaptive thinning for bivariate scattered data
• Multilevel scattered data approximation by adaptive domain decomposition
• Multistep scattered data interpolation using compactly supported radial basis functions
• A multilevel block incomplete Cholesky preconditioner for solving normal equations in linear least squares problems
• Least squares approximation by splines with free knots
• Nonuniform web-splines
• Local error estimates for radial basis function interpolation of scattered data
• Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage
• Accuracy and Stability of Numerical Algorithms
• Computational Methods for Inverse Problems
• Smoothing noisy data with spline functions
• Least squares scattered data fitting by truncated SVDs
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