Convergence of Derivatives of Optimal Nodal Splines |
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Authors: | Vittoria Demichelis |
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Institution: | Department of Mathematics, University of Turin, Via Carlo Alberto 10, I-10123, Turin, Italy |
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Abstract: | Optimal nodal spline interpolantsWfof ordermwhich have local support can be used to interpolate a continuous functionfat a set of mesh points. These splines belong to a spline space with simple knots at the mesh points as well as atm−2 arbitrary points between any two mesh points and they reproduce polynomials of orderm. It has been shown that, for a sequence of locally uniform meshes, these splines converge uniformly for anyfCas 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 ofDjWftoDjfforfCsandj=1, …, s<m. In addition we give a bound forDrWfwiths<r<m. Finally, we use optimal nodal spline interpolants for the numerical evaluation of Cauchy principal value integrals. |
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