A Natural Formulation of Quasi-Interpolation by Multivariate Splines

DOI10.2307/2046468zbMath0656.41005OpenAlexW4244183357MaRDI QIDQ3803599

Harvey Diamond, Charles K. Chui

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2046468

zbMATH Keywords

Neumann series expansiondiscrete functionFix-Strang conditionsmultivariate spline seriesquasi-interpolation formula

Mathematics Subject Classification ID

Multidimensional problems (41A63) Interpolation in approximation theory (41A05) Spline approximation (41A15)

Related Items (37)

Quasi-regression with shrinkage ⋮ The polynomials in the linear span of integer translates of a compactly supported function ⋮ Quasi-regression ⋮ Divergence-free quasi-interpolation ⋮ Quasi-interpolation in the Fourier algebra ⋮ Shape-preserving quasi-interpolation and interpolation by box spline surfaces ⋮ Super-resolution wavelets for recovery of arbitrarily close point-masses with arbitrarily small coefficients ⋮ Wavelet thresholding for recovery of active sub-signals of a composite signal from its discrete samples ⋮ Construction techniques for highly accurate quasi-interpolation operators ⋮ Approximation on variable exponent spaces by linear integral operators ⋮ Pointwise and uniform approximation by multivariate neural network operators of the max-product type ⋮ A convergent iterated quasi-interpolation for periodic domain and its applications to surface PDEs ⋮ Optimal adaptive sampling recovery ⋮ Detection of thermal bridges from thermographic images by means of image processing approximation algorithms ⋮ Constructing radial kernels with higher-order generalized Strang-Fix conditions ⋮ Spline manipulations for empirical mode decomposition (EMD) on bounded intervals and beyond ⋮ A characterization of multivariate quasi-interpolation formulas and its applications ⋮ B-spline quasi-interpolant representations and sampling recovery of functions with mixed smoothness ⋮ Algorithms for generating B-nets and graphically displaying spline surfaces on three- and four-directional meshes ⋮ Multivariate Monte Carlo Approximation Based on Scattered Data ⋮ Bernstein-Bézier representation and near-minimally normed discrete quasi-interpolation operators ⋮ Quasi-interpolation with translates of a function having noncompact support ⋮ Quasi-interpolation projectors for box splines ⋮ Adaptive sampling recovery of functions with bounded modulus of smoothness ⋮ Cardinal interpolation with differences of tempered functions ⋮ A general method for constructing quasi-interpolants from B-splines ⋮ B-spline quasi-interpolation on sparse grids ⋮ Local Approximation by Certain Spaces of Exponential Polynomials, Approximation Order of Exponential Box Splines, and Related Interpolation Problems ⋮ Minimizing the quasi-interpolation error for bivariate discrete quasi-interpolants ⋮ Non-linear sampling recovery based on quasi-interpolant wavelet representations ⋮ A general framework for local interpolation ⋮ Quasi-interpolants from spline interpolation operators ⋮ Interpolation by Multivariate Splines ⋮ A progressive construction of univariate spline quasi-interpolants on uniform partitions ⋮ Assessing linearity in high dimensions. ⋮ Max-product type multivariate sampling operators and applications to image processing ⋮ Approximation in VLSI simulation

Cites Work

• A multivariate analog of Marsden's identity and a quasi-interpolation scheme
• Spline approximation by quasiinterpolants
• On the approximation order from certain multivariate spline spaces
• Controlled Approximation and a Characterization of the Local Approximation Order
• Cardinal Interpolation by Multivariate Splines
• Unnamed Item

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