Scaling technique for Partition-Nekrasov matrices
Scaling technique for Partition-Nekrasov matrices
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DOI：
10.1016/j.amc.2015.08.136
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发表时间：
2015-11
期刊：
影响因子：
--
通讯作者：
T. Szulc;L. Cvetković;M. Nedovic
中科院分区：
文献类型：
--
作者：
T. Szulc;L. Cvetković;M. Nedovic
众所周知，对于给定的H-矩阵A，存在一个对角非奇异矩阵，它将A（通过从右乘）缩放为严格对角占优（SDD）矩阵。H-矩阵的子类可以完全由相应的对角缩放矩阵的形式来表征。然而，对于某些应用，没有必要具有这样的完整表征。只要找到至少一个能完成这项工作的缩放矩阵就足够了。本文的目的是为H-矩阵的一个特殊子类--分块Nekrasov矩阵给出一种构造对角尺度矩阵的方法。作为这种缩放方法的应用，我们得到相应的舒尔补矩阵的特征值定位，只使用原始矩阵的条目。
It is well-known that for a given H-matrixAthere exists a diagonal nonsingular matrix that scalesA(by multiplying it from the right) to a strictly diagonally dominant (SDD) matrix. There are subclasses of H-matrices that can be fully characterised by the form of the corresponding diagonal scaling matrices. However, for some applications, it is not necessary to have such full characterisation. It is sufficient to find at least one scaling matrix that will do the job. The aim of this paper is to present a way of constructing a diagonal scaling matrix for one special subclass of H-matrices called Partition-Nekrasov matrices. As an application of this scaling approach, we obtain eigenvalue localisation for the corresponding Schur complement matrix, using only the entries of the original matrix.