Local approximation on surfaces with discontinuities, given limited order Fourier coefficients

DOI10.1016/j.cam.2007.09.022zbMath1147.65011OpenAlexW2025676069MaRDI QIDQ932742

R. K. Wright

Publication date: 11 July 2008

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2007.09.022

zbMATH Keywords

surfacespline approximationFourier coefficientsjump discontinuitieslocal approximationbivariate function

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Spline approximation (41A15) Numerical methods for trigonometric approximation and interpolation (65T40) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Computer-aided design (modeling of curves and surfaces) (65D17)

Cites Work

• Unnamed Item
• On the Gibbs phenomenon. I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function
• The resolution of the Gibbs phenomenon for ``spliced functions in one and two dimensions
• Local spline approximation of discontinuous functions and location of discontinuities, given low-order Fourier coefficient information.
• A robust method for accurately representing nonperiodic functions given Fourier coefficient information
• On uniform approximation by splines
• On the Gibbs Phenomenon and Its Resolution
• Accurate Reconstructions of Functions of Finite Regularity from Truncated Fourier Series Expansions
• The \(L_\infty\)-norm of the \(L_2\)-spline projector is bounded independently of the knot sequence: A proof of de Boor's conjecture

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