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线性等式和不等式组的求解及其非相容性特征

魏紫銮,张宝康   

  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

魏紫銮,张宝康. 线性等式和不等式组的求解及其非相容性特征[J]. 计算数学, 1983, 5(2): 187-194.

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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