二维连续分片线性绝对值模型

Absolute value model for 2 -D continuous piecewise linear functions

因为连续分片线性常规模型使用过多参数 ,所以研究它的紧凑模型很有必要。通过分析连续分片线性函数本身而不仅仅分析函数的定义域 ,采用分解叠加的方式构造出函数的新绝对值紧凑模型。模型的有效性被严格证明。证明过程中还给出表示已有连续分片线性函数的算法。新模型有两个明显的优点 :一是可以直观简便地表示所有二维空间上连续分片线性函数 ;二是便于给出用连续分片线性函数逼近连续非线性函数的算法。

Conventional models for continuous piecewise linear (PWL) functions have too many parameters which cannot compactly represent PWL functions. This paper presents an absolute value model of 2 -D continuous PWL functions using decomposition and superposition, which analyzes the structure of PWL functions instead of their subdomains. The availability of the model has been proven strictly. In fact an algorithm is also presented to represent existing PWL functions in the course of the proof. The feature of the novel model is as follows: 1) it is more convenient to represent a known PWL function; 2) it is easier to design the nonlinear approximation algorithm by means of this representation.