An adaptive algorithm for multivariate approximation giving optimal convergence rates

DOI10.1016/0021-9045(79)90021-2zbMath0411.41008OpenAlexW1966895140MaRDI QIDQ1259796

John R. Rice, Carl De Boor

Publication date: 1979

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

Full work available at URL: https://doi.org/10.1016/0021-9045(79)90021-2

zbMATH Keywords

numerical methodsquadraturedegree of approximationpiecewise polynomial approximationmultidimensional problems

Mathematics Subject Classification ID

Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25) Spline approximation (41A15) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (9)

An optimal sequential algorithm for the uniform approximation of convex functions on \([0,1^ 2\)] ⋮ Uniform tree approximation by global optimization techniques ⋮ Remarks on algorithm 006: An adaptive algorithm for numerical integration over an N-dimensional rectangular region ⋮ Representation complexity of adaptive 3D distance fields ⋮ Approximation by linear combinations of multivariate B-splines ⋮ Adaptive approximation by multivariate smooth splines ⋮ On the degree of nonlinear spline approximation in Besov-Sobolev spaces ⋮ Estimates for the modulus of smoothness ⋮ Sequential algorithms of optimal order global error for the uniform recovery of functions with monotone (r-1) derivatives

Cites Work

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• Adaptive approximation
• Splines (with optimal knots) are better
• On the Degree of Convergence of Piecewise Polynomial Approximation on Optimal Meshes

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