摘要
在电网络理论［１．２］中，考虑约束方程ＡＸ＋ｙ＝ｂ，Ｘ∈Ｌ，ｙ∈Ｌ⊥，其中Ａ∈Ｃｎ×ｎ，子空间，ｂ∈Ｃｎ．当Ａ有小扰动矩阵Ｅ，ｂ有小扰动△ｂ时，存在ｘ，ｙ满足（Ａ＋Ｅ）ｘ＋ｙ＝ｂ十△ｂ，ｘ∈Ｌ，ｙ∈Ｌ⊥，本文给出双扰动约束方程的扰动分析，并证明了条件数在理论解ｘ和扰动解ｘ的相对误差界中的最优性，改进了文献［８］中的结果．
For a constrained system Ax + y = b, x∈L,y∈L, where A ∈ Cn×n, a subspace L Cn, and b ∈Cn, if A has a small perturbation matrix E, b has a small perturbation b, then x, y satisfy(A + E)x + y = b + b,x∈ L,y∈ L, Such systems are discussed in electrical network theory[1,2].This paper gives the perturbation analysis of the doubly perturbed system, an.d shows that the condition number of relative error bounds of the theoretical solution x and f the perturbation solution x is the minimum in some sense, which improves previous results[8].
出处
《上海师范大学学报（自然科学版）》
1996年第2期9-14,共6页
Journal of Shanghai Normal University(Natural Sciences)
关键词
约束方程
扰动解
条件数
constrained system
condition number
perturbation solution
