Convergence of spline interpolation processes and conditionality of systems of equations for spline construction
Yu. S. Volkovab
a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
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.
splines, interpolation, convergence, projector norm, construction algorithms, conditionality.
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Sbornik: Mathematics, 2019, 210:4, 550–564
MSC: Primary 41A15; Secondary 65D07
Received: 05.05.2017 and 17.07.2018
Yu. S. Volkov, “Convergence of spline interpolation processes and conditionality of systems of equations for spline construction”, Mat. Sb., 210:4 (2019), 87–102; Sb. Math., 210:4 (2019), 550–564
Citation in format AMSBIB
\paper Convergence of spline interpolation processes and conditionality of systems of equations for spline construction
\jour Mat. Sb.
\jour Sb. Math.
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