A family of nonoscillatory 6point interpolatory

Authors: Rosa Donat Sergio LópezUreña Maria Santágueda

Publish Date: 2017/02/14

Volume: 43, Issue: 4, Pages: 849-883

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Abstract

In this paper we propose and analyze a new family of nonlinear subdivision schemes which can be considered nonoscillatory versions of the 6point DeslauriesDubuc DD interpolatory scheme just as the Power p schemes are considered nonlinear nonoscillatory versions of the 4point DD interpolatory scheme Their design principle may be related to that of the Power p schemes and it is based on a weighted analog of the Power p mean We prove that the new schemes reproduce exactly polynomials of degree three and stay ’close’ to the 6point DD scheme in smooth regions In addition we prove that the first and second difference schemes are well defined for each member of the family which allows us to give a simple proof of the uniform convergence of these schemes and also to study their stability as in 19 22 However our theoretical study of stability is not conclusive and we perform a series of numerical experiments that seem to point out that only a few members of the new family of schemes are stable On the other hand extensive numerical testing reveals that for smooth data the approximation order and the regularity of the limit function may be similar to that of the 6point DD scheme and larger than what is obtained with the Power p schemes

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