Spectral methods refer to the use of eigenvalues, eigenvectors,
singular values and singular vectors and they are widely used in
Engineering, Applied Mathematics and Statistics. More recently,
spectral methods have found numerous applications in Computer
Science to ""discrete"" as well ""continuous"" problems. Spectral
Algorithms describes modern applications of spectral methods, and
novel algorithms for estimating spectral parameters. The first part
of the book presents applications of spectral methods to problems
from a variety of topics including combinatorial optimization,
learning and clustering. The second part is motivated by efficiency
considerations. A feature of many modern applications is the
massive amount of input data. While sophisticated algorithms for
matrix computations have been developed over a century, a more
recent development is algorithms based on ""sampling on the y""
from massive matrices. Good estimates of singular values and low
rank approximations of the whole matrix can be provably derived
from a sample. The main emphasis in the second part of the book is
to present these sampling methods with rigorous error bounds. It
also presents recent extensions of spectral methods from matrices
to tensors and their applications to some combinatorial
optimization problems.
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