一种设计分解的正确性证明

二维变量化设计系统可以用含有n个未知数、m个方程的非线性方程组表示．通过设计分解可以提高几何约束求解的效率和数值稳定性．给出了一种基于图论的设计分解方法及其正确性证明．该方法可以（1）处理结构欠约束系统的分解；（2）检测出冗余约束．分解算法在有限步内终止，其结果是结构相容的

The Correctness Proof of a Decomposing Approach

Mathematically a 2Dconstrained design system can be modeled by mindependent nonlinear equa－tions with n design variables and the design process can be viewed as a process ofsolving a geometric constraintsystem．Design decomposition is a highly effective way to improve a geometric constraint solver to make it effi－cient and robust．This paper reports a graph based decomposing approach and gives the correctness proof oftheapproach：（1）this approach can dealwith the decomposition ofstructurally under－constrained systems，（2）thisapproach can detect structurally over－constrained systems，（3）the approach can terminate within finite numberofsteps，and（4）the solving steps obtained through the decomposing approach are structurally consistent．