On Error Estimates of Local Approximation by Splines
2020
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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