Inequalities of Kolmogorov type and estimates of spline interpolation on periodic classes \(W^ m_ 2\)

DOI10.1007/BF01139609zbMath0753.42003MaRDI QIDQ1813363

A. Yu. Shadrin

Publication date: 25 June 1992

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

zbMATH Keywords

spline interpolationperiodic functionsinequalities of Kolmogorov typeperiodic classes \(W^ m_ 2\)periodic polynomial spline

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Trigonometric approximation (42A10) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Spline approximation (41A15)

Related Items

The Landau-Kolmogorov problem on a finite interval in the Taikov case, Optimal recovery on classes of functions analytic in an annulus, Some remarks on spectral convergence and stability of iso-geometric analysis, On Hardy-Littlewood-Pólya and Taikov type inequalities for multiple operators in Hilbert spaces, Explicit error estimates for spline approximation of arbitrary smoothness in isogeometric analysis, Stable summation of orthogonal series with noisy coefficients.

Cites Work

• Exact error bound of approximation by interpolating splines in \(L\)-metric on the classes \(W^r_p(1\leq p<\infty)\) of periodic functions
• Approximation by periodic spline interpolants on uniform meshes
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