Condition numbers and equilibration of matrices
Condition numbers and equilibration of matrices
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DOI：
10.1007/bf02165096
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发表时间：
1969-12
影响因子：
2.1
通讯作者：
A. Sluis
中科院分区：
文献类型：
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作者：
A. Sluis
在数值线性代数中，满足条件数[[AII [] A-11 [和类似的量，例如（max [a，i [）[[A-1H和[[Ai [Al []，其中A=（a，i）并且Ai是A的第i列。规范是非常多样的。然后，问题是确定A的行和/或列缩放，使所考虑的量最小化。这是本文的目的是指定一类这样的数量，这些标度可以明确给出。所得结果是文[2]中某些结果的推广。它们也适用于非方阵。所有的证明都是完全初等的。
In numerical linear algebra one meets condition numbers [[AII [] A-11 [and similar quantities such as (max [a, i [)[[A-1H and [[Ai [[[[Al [], where A=(a, i) and A i is the/'-th column of A. The norms are very diverse. The problem then is to determine a row-and/or column-scaling of A which minimizes the quantity under consideration. It is the purpose of this paper to specify a class of such quantities for which those scalings can be given explicitly. The results will be extensions of some results in [2]. They will also hold for non-square matrices. All proofs will be completely elementary.