Almost sure convergence of smoothing \(D^ m\)-splines of noisy data

DOI10.1007/BF01385698zbMath0798.41001MaRDI QIDQ1326492

Rémi Arcangéli, Bernard Ycart

Publication date: 6 June 1994

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

Full work available at URL: https://eudml.org/doc/133763

zbMATH Keywords

random noisesmoothing \(D^ m\)-splines

Mathematics Subject Classification ID

Spline approximation (41A15)

Related Items (11)

Scattered noisy Hermite data fitting using an extension of the weighted least squares method ⋮ Approximation of patches by \(\mathcal C^r\)-finite elements of Powell-Sabin type ⋮ Minimal energy \(C^r\)-surfaces on uniform Powell-Sabin-type meshes for noisy data ⋮ An extension of a bound for functions in Sobolev spaces, with applications to \((m, s)\)-spline interpolation and smoothing ⋮ Filling holes with shape preserving conditions ⋮ Approximation by smoothing variational vector splines for noisy data ⋮ An approximation problem of noisy data by cubic and bicubic splines ⋮ Minimal energy surfaces on Powell-Sabin type triangulations ⋮ A hole filling method for surfaces by using \(\mathcal C^1\)-Powell-Sabin splines. Estimation of the smoothing parameters ⋮ Discrete approximation by variational vector splines for noisy data ⋮ Probabilistic analysis on the splitting-shooting method for image transformations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Estimations de l'erreur d'approximation par splines d'interpolation et d'adjustement d'ordre (m,s). (Approximation error estimates for interpolating and smoothing (m,s)-splines)
• Error bounds for derivative estimates based on spline smoothing of exact or noisy data
• Double stochastic integrals, random quadratic forms and random series in Orlicz spaces
• Convergence rates for multivariate smoothing spline functions
• Order-of-magnitude bounds for expectations involving quadratic forms
• General Lagrange and Hermite interpolation in \(R^n\) with applications to finite element methods
• Multivariate Smoothing Spline Functions
• Sums of independent Banach space valued random variables

This page was built for publication: Almost sure convergence of smoothing \(D^ m\)-splines of noisy data