EAN: 9783031116971

SPRINGERBRIEFS IN MATHEMATICS LOCATING EIGENV...

This book focuses on linear time eigenvalue location algorithms for graphs. This subject
relates to spectral graph theory  a field that combines tools and concepts of linear algebra
and combinatorics  with applications ranging from image processing and data analysis to
molecular descriptors and random walks. It has attracted a lot of attention and has since
emerged as an area on its own. Studies in spectral graph theory seek to determine properties of
a graph through matrices associated with it. It turns out that eigenvalues and eigenvectors
have surprisingly many connections with the structure of a graph. This book approaches this
subject under the perspective of eigenvalue location algorithms. These are algorithms that 
given a symmetric graph matrix M and a real interval I  return the number of eigenvalues of M
that lie in I. Since the algorithms described here are typically very fast  they allow one to
quickly approximate the value of any eigenvalue  which is a basic step in most applications of
spectral graph theory. Moreover  these algorithms are convenient theoretical tools for proving
bounds on eigenvalues and their multiplicities  which was quite useful to solve longstanding
open problems in the area. This book brings these algorithms together  revealing how similar
they are in spirit  and presents some of their main applications. This work can be of special
interest to graduate students and researchers in spectral graph theory  and to any
mathematician who wishes to know more about eigenvalues associated with graphs. It can also
serve as a compact textbook for short courses on the topic.

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