Abstract by Seong-Eun Cho
Efficiently approximating the eigenvalues of a matrix or graph
The eigenvalues of a matrix or graph contain valuable information about its characteristics and properties. However, it is computationally costly to find these values especially as the size of the matrix gets large. Gershgorin's Circle Theorem allows us to find regions in the complex plane in which each eigenvalue must lie. Using an isospectral graph reduction algorithm, which allows us to reduce the size of a graph or matrix while preserving its eigenvalues, it is possible to greatly reduce the area of the Gershgorin regions, hence allowing for a better approximation of the eigenvalues. We will show that by using machine learning algorithms it is possible to reduce specific rows of a matrix (or nodes of a graph) to most efficiently decrease the area of the Gershgorin regions.