A multivariate analog of Marsden's identity and a quasi-interpolation scheme

DOI10.1007/BF01890557zbMath0623.41009OpenAlexW2058672562MaRDI QIDQ1091549

Ming-Jun Lai, Charles K. Chui

Publication date: 1987

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01890557

zbMATH Keywords

Fourier transformmultivariate polynomialbox splinesmultivariate order

Mathematics Subject Classification ID

Multidimensional problems (41A63) Spline approximation (41A15)

Related Items (17)

Divergence-free quasi-interpolation ⋮ Constructing radial kernels with higher-order generalized Strang-Fix conditions ⋮ Effortless quasi-interpolation in hierarchical spaces ⋮ A characterization of multivariate quasi-interpolation formulas and its applications ⋮ Raising the approximation order of multivariate quasi-interpolants ⋮ 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 ⋮ Linear independence of the translates of an exponential box spline ⋮ Quasi-interpolation projectors for box splines ⋮ A general method for constructing quasi-interpolants from B-splines ⋮ B-spline quasi-interpolation on sparse grids ⋮ The method of virtual components in the multivariate setting ⋮ Minimizing the quasi-interpolation error for bivariate discrete quasi-interpolants ⋮ Quasi-interpolation for analysis-suitable T-splines ⋮ A Natural Formulation of Quasi-Interpolation by Multivariate Splines ⋮ A progressive construction of univariate spline quasi-interpolants on uniform partitions

Cites Work

• B-splines from parallelepipeds
• Bivariate box splines and smooth pp functions on a three direction mesh
• An identity for spline functions with applications to variation diminishing spline approximation
• On the approximation order from certain multivariate spline spaces
• Approximation by Smooth Multivariate Splines
• Approximation Order from Bivariate C 1 -Cubics: A Counterexample
• Controlled Approximation and a Characterization of the Local Approximation Order
• Cardinal Interpolation by Multivariate Splines
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