等谱图约简与矩阵谱的改进估计
Isospectral Graph Reductions and Improved Estimates of Matrices' Spectra
摘要：
通过等谱图约简过程，可以将图的邻接矩阵约简为较小的矩阵，同时保持图的谱直到某个已知集合。然后可以通过考虑与缩减矩阵相关联的Gershgorin型估计来估计原始矩阵的谱。本文的主要结果是，与Gershgorin，Brauer，Brualdi和Varga的特征值估计提高矩阵大小减少。此外，鉴于这种估计随着每次连续的减少而改进，也可以通过重复使用该过程来以增加的精度估计矩阵的特征值。
英文摘要：
Via the process of isospectral graph reduction the adjacency matrix of a graph can be reduced to a smaller matrix while its spectrum is preserved up to some known set. It is then possible to estimate the spectrum of the original matrix by considering Gershgorin-type estimates associated with the reduced matrix. The main result of this paper is that eigenvalue estimates associated with Gershgorin, Brauer, Brualdi, and Varga improve as the matrix size is reduced. Moreover, given that such estimates improve with each successive reduction, it is also possible to estimate the eigenvalues of a matrix with increasing accuracy by repeated use of this process.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
