Explicit error bounds for spline interpolation on a uniform partition
The authors have shown that \(C^0_n (u, \upsilon)\) and \(D^0_n (\upsilon)\) are the best constants in the inequalities (1.6) and (1.7) defined on page 3 of this paper. They also present explicit expressions for these constants. In case \(k>0\), they present explicit expressions to bound the constants. Giving some preliminaries, they also establish some useful properties of the kernels \(K^k_n (u, \upsilon, \theta)\). Precisely, this paper considers the optimality and the evaluation of the constants that appear in the expressions of error bounds for interpolating spline functions over a uniform mesh of real line when the nodes are uniformly shifted. Some similar results have already been presented by I. J. Schoenberg in 1976.
scientific article; zbMATH DE number 782140
scientific article