Convergence of derivatives of optimal nodal splines

[摘要] Optimal nodal spline interpolants Wf of order m which have local support can be used to interpolate a continuous function fat a set of mesh points. These splines belong to a spline space with simple knots at the mesh points as well as at m-2 arbitrary points between any two mesh points and they reproduce polynomials of order m. It has been shown that, for a sequence of locally uniform meshes, these splines converge uniformly for any f is an element of C as the mesh norm tends to zero. In this paper, we derive a set of sufficient conditions on the sequence of meshes for the uniform convergence of D(j)Wf to D(j)f for f is an element of C-5 and j=1,..., s

[发布日期] 1997-03-01