How small can one make the derivatives of an interpolating function?

DOI10.1016/0021-9045(75)90043-XzbMath0293.41007MaRDI QIDQ1212209

Carl De Boor

Publication date: 1975

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

Mathematics Subject Classification ID

Numerical interpolation (65D05) Interpolation in approximation theory (41A05) Spline approximation (41A15) Numerical methods for ordinary differential equations (65L99)

Related Items (14)

Higher-order estimates for fully nonlinear difference equations. I ⋮ Convergence of regularized spline approximants to solutions of initial and boundary value problems for ODE ⋮ Extremal functional -interpolation on an arbitrary mesh on the real axis ⋮ On an interpolation problem with the smallest \(L_2\)-norm of the Laplace operator ⋮ Local extremal interpolation on the semiaxis with the least value of the norm for a linear differential operator ⋮ Approximation rates for interpolation of Sobolev functions via Gaussians and allied functions ⋮ Efficient computation of Favard constants and their connection to Euler polynomials and numbers ⋮ Lagrange interpolation on a lattice: Bounding derivatives by divided differences ⋮ Extension criteria for homogeneous Sobolev spaces of functions of one variable ⋮ Sobolev functions on closed subsets of the real line ⋮ One estimate for divided differences and its applications ⋮ Bounds for divided differences of grid function ⋮ Error bounds for derivative estimates based on spline smoothing of exact or noisy data ⋮ Favard's interpolation problem in one or more variables

Cites Work

• Spline approximation by quasiinterpolants
• \(H^{m,p}\)-extensions by \(H^{m,p}\)-splines
• Sur l'interpolation
• Characterizations of Functions with Higher Order Derivatives in ℒ p
• Unnamed Item

This page was built for publication: How small can one make the derivatives of an interpolating function?