Bivariate \(C ^{2}\) cubic spline quasi-interpolants on uniform Powell-Sabin triangulations of a rectangular domain

DOI10.1007/s10444-011-9178-3zbMath1251.41001OpenAlexW2081235129MaRDI QIDQ429797

Sara Remogna

Publication date: 20 June 2012

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

Full work available at URL: https://doi.org/10.1007/s10444-011-9178-3

zbMATH Keywords

spline approximationquasi-interpolation operatormulti-box spline

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Interpolation in approximation theory (41A05)

Related Items (17)

Near-best \(C^2\) quartic spline quasi-interpolants on type-6 tetrahedral partitions of bounded domains ⋮ Point and differential \(C^1\) quasi-interpolation on three direction meshes ⋮ Construction of a normalized basis of a univariate quadratic $C^1$ spline space and application to the quasi-interpolation ⋮ Quasi-interpolation by \(C^1\) quartic splines on type-1 triangulations ⋮ Superconvergent quadratic spline quasi-interpolants on Powell-Sabin partitions ⋮ Super-smooth cubic Powell-Sabin splines on three-directional triangulations: B-spline representation and subdivision ⋮ Increasing the approximation order of spline quasi-interpolants ⋮ Superconvergent spline quasi-interpolants and an application to numerical integration ⋮ \(\mathcal{C}^1\) cubic splines on Powell-Sabin triangulations ⋮ Hermite spline interpolation on a three direction mesh from Powell-Sabin and Hsieh-Clough-Tocher finite elements ⋮ Trivariate near-best blending spline quasi-interpolation operators ⋮ A trivariate near-best blending quadratic quasi-interpolant ⋮ Construction of superconvergent quasi-interpolants using new normalized \(C^2\) cubic B-splines ⋮ On the construction of trivariate near-best quasi-interpolants based on \(C^2\) quartic splines on type-6 tetrahedral partitions ⋮ \(C^1\)-quartic butterfly-spline interpolation on type-1 triangulations ⋮ Superconvergent \(C^1\) cubic spline quasi-interpolants on Powell-Sabin partitions ⋮ On spline quasi-interpolation through dimensions

Cites Work

• Scattered data fitting by direct extension of local polynomials to bivariate splines
• Some performances of local bivariate quadratic \(C^1\) quasi-interpolating splines on nonuniform type-2 triangulations
• \(C^{2}\) piecewise cubic quasi-interpolants on a 6-direction mesh
• On near-best discrete quasi-interpolation on a four-directional mesh
• Surface subdivision schemes generated by refinable bivariate spline function vectors
• Bernstein-Bézier representation and near-minimally normed discrete quasi-interpolation operators
• Approximating partial derivatives of first and second order by quadratic spline quasi-interpolants on uniform meshes
• Near-best quasi-interpolants associated with \(H\)-splines on a three-direction mesh
• Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices
• Multi-box splines
• Spline Functions on Triangulations
• Scattered Data Interpolation: Tests of Some Method
• Constructing Good Coefficient Functionals for Bivariate C 1 Quadratic Spline Quasi-Interpolants
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