H-matrix theory vs. eigenvalue localization
H-matrix theory vs. eigenvalue localization
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DOI：
10.1007/s11075-006-9029-3
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发表时间：
2006-08
影响因子：
2.1
通讯作者：
L. Cvetković
中科院分区：
文献类型：
--
作者：
L. Cvetković
The eigenvalue localization problem is very closely related to the-matrix theory. The most elegant example of this relation is the equivalence between the Geršgorin theorem and the theorem about nonsingularity of SDD (strictly diagonally dominant) matrices, which is a starting point for further beautiful results in the book of Varga [19]. Furthermore, the corresponding Geršgorin-type theorem is equivalent to the statement that each matrix from a particular subclass of-matrices is nonsingular. Finally, the statement that all eigenvalues of a given matrix belong to minimal Geršgorin set (defined in [19]) is equivalent to the statement that every-matrix is nonsingular. Since minimal Geršgorin set remained unattainable, a lot of different Geršgorin-type areas for eigenvalues has been developed recently. Along with them, a lot of new subclasses of-matrices were obtained. A survey of recent results in both areas, as well as their relationships, will be presented in this paper.
