Exact values of best approximations for classes of periodic functions by splines of deficiency 2

DOI10.1134/S0001434609030237zbMath1204.41018OpenAlexW1974282175MaRDI QIDQ1033958

Nataliia Viktorivna Parfinovych, Vladislav F. Babenko

Publication date: 10 November 2009

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434609030237

zbMATH Keywords

modulus of continuityperiodic functionKolmogorov widthbest \(L_{1}\)-approximationpolynomial spline of deficiency 2rearrangement-invariant set

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Best approximation, Chebyshev systems (41A50) Spline approximation (41A15) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46) Best constants in approximation theory (41A44)

Related Items (3)

On the exact values of the best approximations of classes of differentiable periodic functions by splines ⋮ Widths of weighted Sobolev classes with constraints \(f(a) = \cdots = f^{(k-1)}(a) = f^{(k)}(b) = \cdots = f^{(r-1)}(b) = 0\) and the spectra of nonlinear differential equations ⋮ Exact values of the best \((\alpha,\beta)\)-approximations for the classes of convolutions with kernels that do not increase the number of sign changes

Cites Work

• Approximations, widths and optimal quadrature formulae for classes of periodic functions with rearrangements invariant sets of derivatives
• On n-widths of periodic functions
• Diameters of some classes of differable periodic functions in the space L
• Inequalities for upper bounds of functionals
• Complexity of approximation problems
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