A Feasibility Result for Interval Gaussian Elimination Relying on Graph Structure
A Feasibility Result for Interval Gaussian Elimination Relying on Graph Structure
复制标题
基于图结构的区间高斯消去法的可行性结果
DOI：
10.1007/978-3-7091-6280-4_8
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
A. Frommer
中科院分区：
文献类型：
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作者：
A. Frommer
设A =（aij）∈|| Rnxnnxn是一个区间矩阵，即每个元素都是一个紧的真实的区间。“矩阵”A ∈|本文将具有真实的系数的Rn × nnxn称为点矩阵，向量也采用类似的符号和术语。Letb∈||是区间向量。我们感兴趣的是计算包含解集$$\开始{array}{*{20}{r}} {S：= \{ x \in {\mathbb{R}^n}：存在点矩阵A \in A } \\ {和点向量B \in B\}使得Ax = B\}。{array}$$
LetA= (aij) ∈ ||Rnxnnxnbe aninterval matrix, i.e. each entry is a compact real interval. ‘Usual’ matricesA∈ |Rnxnnxnwith real coefficients will be calledpoint matricesin this paper, and a similar notation and terminology is adopted for vectors. Letb∈ ||Rnxnnbe an interval vector. We are interested in computing an interval vector containing the solution set $$\begin{array}{*{20}{r}} {S : = \{ x \in {\mathbb{R}^n}:there exist a point matrix A \in A } \\ {and a point vector b \in b such that Ax = b\} .} \end{array}$$