New upper bound for the \(B\)-spline basis condition number II. A proof of de Boor's \(2^k\)-conjecture

DOI10.1006/jath.1998.3310zbMath0955.41013OpenAlexW2005812153MaRDI QIDQ1305493

A. Yu. Shadrin, Karl Scherer

Publication date: 11 November 1999

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

Full work available at URL: https://doi.org/10.1006/jath.1998.3310

zbMATH Keywords

B-spline condition numberde Boor's conjecture

Mathematics Subject Classification ID

Spline approximation (41A15)

Related Items (13)

On the best conditioned bases of quadratic polynomials ⋮ Variational multiscale nonparametric regression: smooth functions ⋮ Lower bounds for the approximation with variation-diminishing splines ⋮ An algorithm for solving linear Volterra integro-differential equations ⋮ Robust multigrid solvers for the biharmonic problem in isogeometric analysis ⋮ On the condition of cubic B-splines ⋮ Multigrid methods for isogeometric discretization ⋮ Efficient computation of Favard constants and their connection to Euler polynomials and numbers ⋮ Local approximation from spline spaces on box meshes ⋮ Sharp error estimates for spline approximation: Explicit constants, n-widths, and eigenfunction convergence ⋮ On the \(p\)-norm condition number of the multivariate triangular Bernstein basis ⋮ Interlacing property for B-splines ⋮ On the \(L_1\)-condition number of the univariate Bernstein basis

Cites Work

• A note on the condition numbers of the B-spline bases
• The exact condition of the B-spline basis may be hard to determine
• Marsden's identity
• The B-spline basis in a space of algebraic polynomials
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