Spectrum of some regular graphs with widely spaced modifications
Name
50147586-MIT.pdf
Description
Full printable version
Size
3.62 MB
Format
Adobe PDF
Checksum (MD5)
92b0eb589942bba1881cc87c44061e95
Author(s)
Liu, Xiangwei, 1976-
Advisor(s)
Gilbert Strang.
Date Issued
2001
Publisher
Massachusetts Institute of Technology
Abstract
This thesis has two parts. The first part studies the spectrum of a family of growing trees, we show that the eigenvalues of the adjacency matrix and Laplacian matrix have high multiplicities. As the trees grow, the graphs of those eigenvalues approach a piecewise-constant "Cantor function", which is different from the corresponding properties of the infinite tree. The second part studies the effect of "widely spaced" modifications on the spectrum of some type of structured matrices. We show that by applying those modifications, new eigenvectors that are localized near the components that correspond to the modified rows appear. By knowing the approximate form of those eigenvectors, we also determine a very close (and simple) approximation to the eigenvalues, and then we show that this approximation is indeed the limit as the matrix grows.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.
Includes bibliographical references (p. 71-72).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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