线性方程组正规化及其应用

Normalization of LinearEquations and its Appliation

目的:提出线性方程组Ax=b与ATAx=ATb同解定理,解决Matlab环境中对线性方程组进行分类判断和函数选择的烦琐问题。方法:证明线性方程组同解定理,编写新程序并与已有Matlab程序比较。结果:新程序比较原有程序机器时耗少。结论:同解定理对解线性方程组求解程序设计具有参考价值。

Objective： To put forward a theorem that the linear equation Ax=b is equivalent to the linearequation ArAx=Arb, and simplify the complicated work in Classiiication and discrimination when linear e-quations are solving with Matlab. Methods： To prove the theorem, program a new procedure, and compare the new procedure and the procedure existed in Matlab. Results. The new procedure occupies less time than the procedure existed in Matlab when linear equations are solved. Conclusion. The theorem is valuable {or programming that relates to solving linear equations.