Abstract
Explicit formulas are given for interpolating parabolic splines on a number line interval constructed by J. Favard in 1940. For approximations by these splines in the Sobolev class \(W_{\infty }^{2}\) of twice differentiable functions, estimates for the norm of the second derivative and the approximation error in the uniform metric are established.
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Funding
This work was supported by the Ministry of Science and Higher Education of the Russian Federation, agreement no. 075-02-2023-913, and was performed at the Ural Mathematical Center.
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Translated by I. Ruzanova
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Shevaldin, V.T. On Favard Local Parabolic Interpolating Splines with Additional Knots. Comput. Math. and Math. Phys. 63, 1045–1051 (2023). https://doi.org/10.1134/S0965542523060167
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DOI: https://doi.org/10.1134/S0965542523060167