Spectral Algorithms (Foundations and Trends(r) in Theoretical Computer Science) - Softcover

Kannan, Ravindran; Vempala, Santosh

Softcover

ISBN 10: 1601982747 ISBN 13: 9781601982742

Publisher: Now Publishers, 2009

Synopsis

Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. 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 as "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 of the book 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 fly" 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.

Edition details

• Publisher: Now Publishers
• Publication date: 2009
• ISBN 10: 1601982747
• ISBN 13: 9781601982742
• Binding: Paperback
• Language: English
• Number of pages: 152