Quadratic spline interpolation on uniform meshes. (English) Zbl 0703.41012
For \(h=N^{-1}\) \((N>1)\) and \(f\in C^ 4[0,1]\), the quadratic spline- interpolation problem \(s(ih)=f(ih)\) \((i=0,...,N)\), \(s'(0)=f'(0)\) is considered. A new proof of the known best error estimates \(\| s- f\|_{\infty}=O(h^ 3)\) and \(\| s'-f'\|_{\infty}=O(h^ 2)\) is given. Further it is shown that superconvergence cannot occur for any particular points independent of f except for ih \((i=0,...,N)\).
Reviewer: M.Tasche
MSC:
| 41A15 | Spline approximation |
References:
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