基于超立方体分割的分片线性逼近  

Piecewise linear approximations with a hypercube partition

作　　者：章浩[1] 王书宁[1] 

机构地区：[1]清华大学自动化系,北京100084

出　　处：《清华大学学报（自然科学版）》2008年第1期153-156,共4页Journal of Tsinghua University(Science and Technology)

基　　金：国家自然科学基金资助项目(60674025;60534060);国家"九七三"基础研究项目(2002CB312200)

摘　　要：为了解决复杂非线性系统的建模问题,提出一种基于超立方体分割的分片线性逼近模型。该模型将定义域分割成超立方体,在每个超立方体内用一个线性函数描述原来的非线性函数。再借助格表示形式,通过选择合适的连接得到由这些局部线性函数构成的连续分片线性函数。证明对于任何二阶可导的非线性函数,该模型都能任意精度逼近。因为不用再把每个超立方体都分割成单纯形,该模型有助于构造出更加简单的连续分片线性函数,并能处理复杂的高维问题。A piecewise linear approximation model with a hypercube partition is introduced for modeling complex nonlinear systems. The model partitions the domain into hypercubes, with one linear function used to approximate the origin nonlinear function in each hypercube. Lattice piecewise linear expressions are used to connect all the local linear functions into a continuous piecewise linear function. This model can approximate any twice differentiable nonlinear function to arbitrary precision. Since each hypercube was not partitioned into simplices, this model constructs simpler piecewise linear functions for complex high dimensional functions.

关 键 词：非线性函数逼近 复杂系统 分片线性 

分 类 号：O174.41[理学—数学] TP271.62[理学—基础数学]