'增强找链接'算法--一种新的非线性逼近方法

摘要

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.该算法使用的"链接超平面"模型,也就是以"链接超平面"作为基函数.理论分析表明使用这种基函数的模型表示能力不足,这使"找链接"算法不可能达到最佳逼近.本文在二维空间上弥补了"链接超平面"模型的局限性,经扩充后的模型在二维空间上有充分的表示能力,从理论上保证了扩充后的模型可以达到最佳逼近.仿真实验表明,在参数个数相同的情况下,使用新模型的逼近算法在逼近精度与预测误差两方面都优于使用原模型.%Nonlinear approximation has been widely applied to many fields. As a kind of sime. The algorithm uses the hinging hyperplanes model that uses hinging hyperplanes as basis functions in expansion. By means of theoretically analyzing it is shown that the representation capability of the model is deficient. The deficiency causes the model′s inability to achieve optimal approximation. In this paper the hinging hyperplanes model is extended and the deficiency is remedied at a twodimensional space. The extended model has enough representation capability, which theoretically ensures the possibility to achieve optimal approximation. In simulation, with the same number of parameters, the new algorithm gets bettering algorithm.