Abstract
We consider the so-called simplest formula for local approximation by polynomial splines of order \( n \) (Schoenberg splines). The spline itself and all derivatives except that of the highest order, approximate a given function and its corresponding derivatives with the second order. We show that the jump of the highest derivative of order \( n-1 \); i. e., the value of discontinuity, divided by the meshsize, approximates the \( n \)th derivative of the original function. We found an asymptotic expansion of the jump.
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Funding
The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (Project No. 0314–2019–0013) and with partial financial support by the Russian Foundation for Basic Research (RFBR) and the German Science Foundation (DFG) according to the joint German–Russian research project 19–51–12008.
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Volkov, Y.S., Bogdanov, V.V. On Error Estimates of Local Approximation by Splines. Sib Math J 61, 795–802 (2020). https://doi.org/10.1134/S0037446620050031
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DOI: https://doi.org/10.1134/S0037446620050031