• 论文 •

### 线性等式和不等式组的求解及其非相容性特征

1. 中国科学院计算中心 ,上海计算技术研究所
• 出版日期:1983-02-14 发布日期:1983-02-14

### THE SOLUTION AND CHARACTERIZATION OF INCONSISTENCY OF SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES

1. Wei Zi-luan Computing Center, Academia Sinica Zhang Bao-kang Shanghai Institute of Computing Technology
• Online:1983-02-14 Published:1983-02-14
1.引言 我们考虑以下形式的等式和不等式线性方程组: sum from j=1 to (a_(ij)x_j)=b_i,i=1,2,…,l, (1.1) sum from j=1 to (a_(ij)x_j)≤b_i,i=l+1,…,m.(1.2)对于求解这类问题,较早的算法有消去法和松弛法(即投影法).消去法在[1]中有详细的叙述.由于它每消去一个变量,不等式的个数就急剧地增加,因而不易在计算机上实现.松弛法虽然计算公式比较简单,但由于它的收敛速度较慢,在应用上有一定的局限性,
This paper presents a method for solving systems of linear equations and inequalities,and proves its characterization of inconsistency in a certain sense. If the systems are consis-tent, a feasible extreme point can be found. If not, a point, which has the characterizationof inconsistency, can be found by the method.
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 [1] J. Stoer, C. Witzgall, Convexity and Optimization in Finite Dimensions I, Springer-verlag, New York, 1970． [2] S. Agmon, The relaxation method for linear inequalities, Canadian Journal of Mathematics,6(1954) , 382-392． [3] 244, №5, 1979． ~~ [4] H. W. Kuhn, A. W. Tucker (Eds.), Linear Inequalities and Related systems, Princeton University press, Princeton, N. J., 1956． [5] J. M. Ortega, Iterative solution of nonlinear equations in several variables, New York, Academic press, 1970． [6] M. S. Bazaraa, C. M. Shetty, Foundations of Optimization, Lecture Notes in Economics and Mathematical Systems, No. 122, Springer-Verlag, New York. 1976．
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