Stable summation of orthogonal series with noisy coefficients.

DOI10.1006/JATH.2002.3710zbMath1035.42025OpenAlexW1981096116MaRDI QIDQ1867506

Peter Mathé, Sergei V. Pereverzyev

Publication date: 2 April 2003

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/30a27ec37b400f57f5e1fc2da7d70d57500b1194

zbMATH Keywords

Haar systemGaussian white noiseorthogonal seriesstable summation

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Summability and absolute summability of Fourier and trigonometric series (42A24)

Related Items (5)

Optimal recovery of operator sequences ⋮ Recovery of function from noisy Fourier coefficients with respect to the Haar system ⋮ The minimal radius of Galerkin information for the problem of numerical differentiation ⋮ Estimates of efficiency for two methods of stable numerical summation of smooth functions ⋮ Recovery of continuous functions from their Fourier coefficients known with error

Cites Work

• Stable summation of Fourier-Haar series with approximate coefficients
• Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes
• Minimax estimation via wavelet shrinkage
• Inequalities of Kolmogorov type and estimates of spline interpolation on periodic classes \(W^ m_ 2\)
• Error bounds for tikhonov regularization in hilbert scales
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