一种新的基于两点自适应的多维近似函数性态研究

A New Multivariable Adaptive Approximate Function for Graph Visualization

利用作者提出的“变基底近似”和“泰勒一阶非线性展开”等手段构造了一种基于两点自适应近似函数 ,旨在改善近似函数的精度和扩大近似范围。数值算例表明 :针对变量具有可分离形式和变量耦合程度较弱的函数 ,它具有很好的近似效果。同时 。

By utilizing the concept of 'variable base approximation' and 'Taylor first order nonlinear expansion', the authors propose a new kind of two-point based adaptive approximate function so as to improve the accuracy and to expand the approximate range. Numerical examples show that the approximation is effective for functions whose variables are either decoupled or with less coupling. Meanwhile, the last example points out a fact that it is worthy to study how to construct the approximate function that can solve the problem with strongly coupling variables.