A Fast Randomized Algorithm for the Approximation of Matrices
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Release | : 2007 |
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Release | : 2007 |
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Author | : Per-Gunnar Martinsson |
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Total Pages | : 32 |
Release | : 2006 |
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Author | : Michael W. Mahoney |
Publisher | : |
Total Pages | : 114 |
Release | : 2011 |
Genre | : Computers |
ISBN | : 9781601985064 |
Randomized Algorithms for Matrices and Data provides a detailed overview, appropriate for both students and researchers from all of these areas, of recent work on the theory of randomized matrix algorithms as well as the application of those ideas to the solution of practical problems in large-scale data analysis
Author | : Martin Fürer |
Publisher | : |
Total Pages | : 11 |
Release | : 2004 |
Genre | : Approximation theory |
ISBN | : |
Abstract: "We present a simple randomized algorithm for approximating permanents of random (0-1) matrices. The algorithm with inputs a, [epsilon]> 0 produces an output X[subscript A] with (1-[epsilon])per(A) [or =] X[subscript A] [or =] (1 + [epsilon])per(A) for almost all (0-1) matrices A. For every positive constant [epsilon] 0, the algorithm runs in time O(n2[omega]), i.e., almost linear in the size of the matrix, where [omega] = [omega](n) is any function satisfying [omega](n) - [infinity] as n -> [infinity]. This improves the previous bound of O(n3[infinity]) for such matrices."
Author | : Rajeev Motwani |
Publisher | : Cambridge University Press |
Total Pages | : 496 |
Release | : 1995-08-25 |
Genre | : Computers |
ISBN | : 1139643134 |
For many applications a randomized algorithm is either the simplest algorithm available, or the fastest, or both. This tutorial presents the basic concepts in the design and analysis of randomized algorithms. The first part of the book presents tools from probability theory and probabilistic analysis that are recurrent in algorithmic applications. Algorithmic examples are given to illustrate the use of each tool in a concrete setting. In the second part of the book, each of the seven chapters focuses on one important area of application of randomized algorithms: data structures; geometric algorithms; graph algorithms; number theory; enumeration; parallel algorithms; and on-line algorithms. A comprehensive and representative selection of the algorithms in these areas is also given. This book should prove invaluable as a reference for researchers and professional programmers, as well as for students.
Author | : Ravindran Kannan |
Publisher | : Now Publishers Inc |
Total Pages | : 153 |
Release | : 2009 |
Genre | : Computers |
ISBN | : 1601982747 |
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.
Author | : Lirkov Ivan Dimov |
Publisher | : Springer |
Total Pages | : 524 |
Release | : 2011-01-27 |
Genre | : Computers |
ISBN | : 3642184669 |
This book constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Numerical Methods and Applications, NMA 2010, held in Borovets, Bulgaria, in August 2010. The 60 revised full papers presented together with 3 invited papers were carefully reviewed and selected from numerous submissions for inclusion in this book. The papers are organized in topical sections on Monte Carlo and quasi-Monte Carlo methods, environmental modeling, grid computing and applications, metaheuristics for optimization problems, and modeling and simulation of electrochemical processes.
Author | : Peter Bühlmann |
Publisher | : CRC Press |
Total Pages | : 480 |
Release | : 2016-02-22 |
Genre | : Business & Economics |
ISBN | : 1482249081 |
Handbook of Big Data provides a state-of-the-art overview of the analysis of large-scale datasets. Featuring contributions from well-known experts in statistics and computer science, this handbook presents a carefully curated collection of techniques from both industry and academia. Thus, the text instills a working understanding of key statistical
Author | : László Erdős |
Publisher | : American Mathematical Soc. |
Total Pages | : 239 |
Release | : 2017-08-30 |
Genre | : Mathematics |
ISBN | : 1470436485 |
A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. This manuscript has been developed and continuously improved over the last five years. The authors have taught this material in several regular graduate courses at Harvard, Munich, and Vienna, in addition to various summer schools and short courses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Author | : Per-Gunnar Martinsson |
Publisher | : SIAM |
Total Pages | : 332 |
Release | : 2019-12-16 |
Genre | : Mathematics |
ISBN | : 1611976049 |
Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.