非光滑函数任意精度光滑逼近的存在性

The Existence of Smooth Approximation for Nonsmooth Function

非线性逼近在许多方面有着广泛的应用."找链接"算法作为一种简洁有效的非线性逼近方法有其独特的优势.但是由于该算法所使用的"链接超平面"模型的局限性,导致该算法的逼近结果不是处处光滑的.在"链接超平面"模型基础上,证明了对于一个非光滑函数存在一个处处光滑的逼近函数.

The nonlinear approximation is applied widely to many fields.As a simple and effective approach,the hingefinding algorithm has particular advantages.The algorithm uses the hinging hyperplanes model that uses hinging hyperplanes as basis function in expansion.The deficiency of the model causes that the result of the hingefinding algorithm is not necessarily smooth everywhere.Based on the hinging hyperplanes model,a function which is smooth everywhere exists for an approximating nonsmooth function.