Faster Algorithms Via Approximation Theory: 26 (Foundations and Trends® in Theoretical Computer Science) - Tapa blanda

Vishnoi, Nisheeth K.; Sachdeva, Sushant

 
9781601988201: Faster Algorithms Via Approximation Theory: 26 (Foundations and Trends® in Theoretical Computer Science)
Tapa blanda
ISBN 10: 1601988206 ISBN 13: 9781601988201
Editorial: Now Publishers Inc, 2014

Sinopsis

Faster Algorithms via Approximation Theory illustrates how classical and modern techniques from approximation theory play a crucial role in obtaining results that are relevant to the emerging theory of fast algorithms. The key lies in the fact that such results imply faster ways to approximate primitives such as products of matrix functions with vectors and, to compute matrix eigenvalues and eigenvectors, which are fundamental to many spectral algorithms.The first half of the book is devoted to the ideas and results from approximation theory that are central, elegant, and may have wider applicability in theoretical computer science. These include not only techniques relating to polynomial approximations but also those relating to approximations by rational functions and beyond. The remaining half illustrates a variety of ways that these results can be used to design fast algorithms.Faster Algorithms via Approximation Theory is self-contained and should be of interest to researchers and students in theoretical computer science, numerical linear algebra, and related areas.

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Reseña del editor

Faster Algorithms via Approximation Theory illustrates how classical and modern techniques from approximation theory play a crucial role in obtaining results that are relevant to the emerging theory of fast algorithms. The key lies in the fact that such results imply faster ways to approximate primitives such as products of matrix functions with vectors and, to compute matrix eigenvalues and eigenvectors, which are fundamental to many spectral algorithms. The first half of the book is devoted to the ideas and results from approximation theory that are central, elegant, and may have wider applicability in theoretical computer science. These include not only techniques relating to polynomial approximations but also those relating to approximations by rational functions and beyond. The remaining half illustrates a variety of ways that these results can be used to design fast algorithms. Faster Algorithms via Approximation Theory is self-contained and should be of interest to researchers and students in theoretical computer science, numerical linear algebra, and related areas.

Reseña del editor

Approximation Theory and Fast Algorithms illustrates how classical and modern results from approximation theory play a crucial role in obtaining results that are relevant to the emerging theory of fast algorithms today. For example, it shows how to compute good approximations to matrix-vector products such as Asv; A-1v and exp(-A)v for any matrix A and a vector v.6. It also shows how to speed up algorithms that compute the top few eigenvalues and eigenvectors of a symmetric matrix A. Such primitives are useful for performing several fundamental computations quickly, such as random walk simulation, graph partitioning, solving linear system of equations, and combinatorial approaches to solving semi-definite programs. The algorithms for computing these primitives perform calculations of the form Bu where B is a matrix closely related to A (often A itself) and u is some vector. A key feature of these algorithms is that if the matrix-vector product for A can be computed quickly, e.g., when A is sparse, then Bu can also be computed in essentially the same time. This makes such algorithms particularly relevant for handling the problem of big data. Such matrices capture either numerical data or large graphs, and it is inconceivable to be able to compute much more than a few matrix-vector products on matrices of this size.

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Editorial
Now Publishers Inc
Año de publicación
2014
Idioma
Inglés
ISBN 10 
1601988206
ISBN 13 
9781601988201
Encuadernación
Tapa blanda
Número de páginas
108
Contacto del fabricante
no disponible
Persona responsable
no disponible