Approximation order of bivariate spline interpolation for arbitrary smoothness

DOI10.1016/S0377-0427(98)00004-1zbMath0932.41002MaRDI QIDQ1298490

O. V. Davydov, Frank Zeilfelder, Günther Nürnberger

Publication date: 21 March 2000

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

zbMATH Keywords

order of approximationHermite interpolationbivariate splines

Mathematics Subject Classification ID

Multidimensional problems (41A63) Interpolation in approximation theory (41A05) Rate of convergence, degree of approximation (41A25) Spline approximation (41A15)

Related Items (18)

Hole-filling techniques by using minimal energy surfaces ⋮ Scattered data interpolation based upon bivariate recursive polynomials ⋮ Fitting missing data by means of adaptive meshes of Bézier curves ⋮ Preconditioned conjugate gradient method for finding minimal energy surfaces on Powell-Sabin triangulations ⋮ Filling holes under non-linear constraints ⋮ Approximation of patches by \(\mathcal C^r\)-finite elements of Powell-Sabin type ⋮ Minimal energy \(C^r\)-surfaces on uniform Powell-Sabin-type meshes for noisy data ⋮ Relationship between quality of basis for surface approximation and the effect of applying preconditioning strategies to their resulting linear systems ⋮ Inverse-free recursive multiresolution algorithms for a data approximation problem ⋮ Filling holes using a mesh of filled curves ⋮ Minimal energy \(C^r\)-surfaces on uniform Powell-Sabin type meshes. Estimation of the smoothing parameters ⋮ Interpolation by \(C^1\) splines of degree \(q\geq 4\) on triangulations ⋮ Bivariate spline interpolation with optimal approximation order ⋮ Multiresolution Analysis for Minimal Energy C r -Surfaces on Powell-Sabin Type Meshes ⋮ Chebyshev multivariate polynomial approximation and point reduction procedure ⋮ An explicit quasi-interpolation scheme based on \(C^1\) quartic splines on type-1 triangulations ⋮ Interpolation by spline spaces on classes of triangulations ⋮ Developments in bivarite spline interpolation

Cites Work

• Approximation order of bivariate spline interpolation
• On the approximation power of bivariate splines
• A sharp upper bound on the approximation order of smooth bivariate pp functions
• Approximation power of smooth bivariate pp functions
• Bivariate spline interpolation at grid points
• Interpolation de Lagrange par des splines quadratiques sur un quadrilatère de $\mathbb {R}^2$
• Error analysis in interpolation by bivariate C1-splines
• Lagrange and hermite interpolation by bivariate splines
• Stability of Optimal-Order Approximation by Bivariate Splines over Arbitrary Triangulations
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