Study of the Convergence of Interpolation Processes with Splines of Even Degree

Abstract

We study the convergence of interpolation processes by Subbotin polynomial splines of even degree. We prove that the good conditionality of a system of equations for constructing an interpolation spline via the coefficients of the expansion of the kth derivative in B-splines is equivalent to the convergence of the interpolation process for the kth derivative of the spline in the class of functions with continuous kth derivative.