关于避免吉布斯振荡的C2非线性细分格式
On a C2-nonlinear subdivision scheme avoiding Gibbs oscillations
AI总结：
提出一种新的非线性细分格式以消除间断附近的吉布斯振荡，并证明其收敛性、稳定性和逼近阶，极限函数具有大于1.192的Hölder正则性指数。
摘要：
本文致力于提出并分析一种新的非线性细分格式，该格式可消除间断附近的吉布斯振荡。分析了其收敛性、稳定性和逼近阶。证明了该格式收敛于Hölder正则性指数大于1.192的极限函数。数值估计提供了2.438的Hölder正则性指数。据我们所知，该方案是第一个同时实现控制吉布斯现象且其极限函数正则性指数大于1的方案。
英文摘要：
This paper is devoted to the presentation and the analysis of a new nonlinear subdivision scheme eliminating the Gibbs oscillations close to discontinuities. Its convergence, stability and order of approximation are analyzed. It is proved that this schemes converges towards limit functions of Hölder regularity index larger than 1.192. Numerical estimates provide an Hölder regularity index of 2.438. Up to our knowledge, this scheme is the first one that achieves simultaneously the control of the Gibbs phenomenon and regularity index larger than 1 for its limit functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
