The \(L_p\)-approximation order of surface spline interpolation for \(1\leq p\leq 2\)
The author studies the problem of \(L_p-\) approximation order of surface spline interpolation. In [Constructive Approximation 14, No.3, 429-438 (1998; Zbl 0904.41005)] and [Math.Comp. 70, No.234, 719-737 (2001; Zbl 0973.41005)] respectively, the author obtained upper and lower bounds for the \(L_p-\) approximation order of surface spline interpolation. It is shown here that the \(L_p-\) approximation order of surface spline interpolation equals \(m+\frac {1}{p}\) for \(1\leq p \leq 2\), where \(m\) is an integer parameter which specifies the surface spline. The author also states numerical evidence to support the conjecture that the \(L_p-\) approximation order of surface spline interpolation is \(m+\frac {1}{p}\) for \(2<p \leq \infty\) also.
scientific article; zbMATH DE number 2111560