On 'best' interpolation

DOI10.1016/0021-9045(76)90093-9zbMath0314.41001OpenAlexW2127693013MaRDI QIDQ1220657

Carl De Boor

Publication date: 1976

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(76)90093-9

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Interpolation in approximation theory (41A05)

Related Items (26)

The maximum entropy method on the mean: Applications to linear programming and superresolution ⋮ Smooth and Semismooth Newton Methods for Constrained Approximation and Estimation ⋮ Best approximation and perturbation property in Hilbert spaces ⋮ Best interpolation in a strip. II: Reduction to unconstrained convex optimization ⋮ Approximation by minimum norm interpolants in the disc algebra ⋮ Unnamed Item ⋮ On an interpolation problem with the smallest \(L_2\)-norm of the Laplace operator ⋮ Limits of 𝐻^{𝑘},𝑝-splines ⋮ Efficient computation of Favard constants and their connection to Euler polynomials and numbers ⋮ Duality and well-posedness in convex interpolation^∗) ⋮ A unifying representer theorem for inverse problems and machine learning ⋮ On best constrained interpolation ⋮ Partially finite convex programming. II: Explicit lattice models ⋮ Extension criteria for homogeneous Sobolev spaces of functions of one variable ⋮ Geometric dual formulation for first-derivative-based univariate cubic \(L_{1}\) splines ⋮ Preferred NBV-splines ⋮ Nonlinear classes of splines and variational problems ⋮ Best approximation and unique extension of Lipschitz functions ⋮ Quasi-uniqueness in \(L^\infty\) extremal problems ⋮ Some results on nearest points in normed linear spaces ⋮ Interpolation of scattered data in \(\mathbb{R}^3\) using minimum \(L_p\)-norm networks, \(1 < p < \infty \) ⋮ Sparsest piecewise-linear regression of one-dimensional data ⋮ Smoothest interpolation in the mean ⋮ Duality Mapping for Schatten Matrix Norms ⋮ Favard's interpolation problem in one or more variables ⋮ Constrained \(L_ p\) approximation

Cites Work

• Unnamed Item
• Unnamed Item
• Perfect spline solutions to \(L^\infty\) extremal problems
• Spline solutions to L\(^1\) extremal problems in one and several variables
• R-splines in Banach spaces. I: Interpolation of linear manifolds
• Sur l'interpolation
• A remark concerning perfect splines
• The Existence, Characterization and Essential Uniqueness of Solutions of L ∞ Extremal Problems
• Some variational problems on certain Sobolev spaces and perfect splines

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