Abstract:
This study is a continuation of research on the convergence of interpolation processes with classical polynomial splines of odd degree. It is proved that the problem of good conditionality of a system of equations for interpolation spline construction via coefficients of the expansion of the $k$th derivative in $B$-splines is equivalent to the problem of convergence of the interpolation process for the $k$th spline derivative in the class of functions with continuous $k$th derivatives. It is established that for interpolation with splines of degree $2n-1$, the conditions that the projectors corresponding to the derivatives of orders $k$ and $2n-1-k$ be bounded are equivalent.
Bibliography: 26 titles.
Keywords:splines, interpolation, convergence, projector norm, construction algorithms, conditionality.
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