Generalized Strang-Fix condition for scattered data quasi-interpolation

DOI10.1007/s10444-004-1832-6zbMath1068.65028OpenAlexW2074819117MaRDI QIDQ1773967

Jian Ping Liu, Zong Min Wu

Publication date: 28 April 2005

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-004-1832-6

zbMATH Keywords

convergenceshift-invariant spacequasi-interpolationscattered data approximationradial basis interpolationStrang-Fix condition

Mathematics Subject Classification ID

Numerical smoothing, curve fitting (65D10) Numerical interpolation (65D05) Multidimensional problems (41A63) Rate of convergence, degree of approximation (41A25)

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Cites Work

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• Fourier analysis of the approximation power of principal shift-invariant spaces
• An introduction to Schoenberg's approximation
• A new version of the Strang--Fix conditions
• Shift-invariant spaces and linear operator equations
• Partition of unity and density: A counterexample
• Compactly supported radial functions and the Strang-Fix condition
• Construction techniques for highly accurate quasi-interpolation operators
• On multivariate approximation by integer translates of a basis function
• On quasi-interpolation by radial basis functions with scattered centres
• Compactly supported positive definite radial functions
• Order of linear approximation from shift-invariant spaces
• Approximation by radial basis functions with finitely many centers
• Local error estimates for radial basis function interpolation of scattered data
• Approximation from Shift-Invariant Subspaces of L 2 (ℝ d )
• Radial Basis Function Approximation: from Gridded Centres to Scattered Centres
• Approximation in \(L_p (\mathbb{R}^d)\) from a space spanned by the scattered shifts of a radial basis function

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