In this paper, the properties of a new family of nonlinear dyadic subdivision schemes are presented and studied depending on the conditions imposed to the mean used to rewrite the linear scheme upon which the new scheme is based. The convergence, stability, and order of approximation of the schemes of the family are analyzed in general. Also, the elimination of the Gibbs oscillations close to discontinuities is proved in particular cases. It is proved that these schemes converge towards limit functions that are Hölder continuous with exponent larger than 1. The results are illustrated with several examples.

中文翻译：

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关于一类具有r> 1的正则性C r的非振荡细分方案

在本文中，提出并研究了一系列新的非线性二进细分方案的性质，这些条件取决于对用于重写该新方案的线性方案的均值施加的条件。通常分析该家庭方案的收敛性，稳定性和逼近阶数。此外，在特定情况下，已证明消除了接近不连续点的吉布斯振荡。证明了这些方案收敛于极限函数，该极限函数是Hölder连续且指数大于1的。结果用几个例子说明。