Isospectral Graph Reductions and Improved Estimates of Matrices' Spectra

Details Isospectral Graph Reductions and Improved Estimates of Matrices' Spectra Isospectral Graph Reductions and Improved Estimates of Matrices' Spectra

2009-11-12

arxiv.org/abs/0911.2453v2

Mathematics

Spectral Theory

32 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Isospectral Graph Reductions and Improved Estimates of Matrices' Spectra does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Isospectral Graph Reductions and Improved Estimates of Matrices' Spectra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Isospectral Graph Reductions and Improved Estimates of Matrices' Spectra will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-151149