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A Convergence Result in Nodal Spline Interpolation

โœ Scribed by J.M. Devilliers

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
337 KB
Volume
74
Category
Article
ISSN
0021-9045

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โœฆ Synopsis

In this paper we study the property of uniform convergence for a certain nodal spline interpolation operator. After solving for the corresponding B-spline coefficients from a transposed Vandermonde linear system, we derive a Jacksontype estimate in which the dependence of the associated constants on order and mesh ratio has been explicitly calculated. Sufficient conditions for uniform convergence are then easily obtained. 1993 Academic Press. Inc.

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Convergence of cubic spline interpolation for discontinuous functions are investigated. It is shown that the complete cubic spline interpolation of the Heaviside step function converges in the LP-norm at rate O(h l/p) for quasi-uniform meshes when 1-%< p < oo, and diverges in the Lยฐยฐ-norm when the u