Spectral Algorithms
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Spectral Algorithms
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Author : Ravindran Kannan
language : en
Publisher: Now Publishers Inc
Release Date : 2009
Spectral Algorithms written by Ravindran Kannan and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Computers categories.
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.
Spectral Methods
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Author : Jie Shen
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-25
Spectral Methods written by Jie Shen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-25 with Mathematics categories.
Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.
Spectral Methods
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Author : Claudio Canuto
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-23
Spectral Methods written by Claudio Canuto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-23 with Science categories.
Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.
Spectral Methods
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Author : Claudio Canuto
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-30
Spectral Methods written by Claudio Canuto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-30 with Mathematics categories.
Following up the seminal Spectral Methods in Fluid Dynamics, Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries. These types of spectral methods were only just emerging at the time the earlier book was published. The discussion of spectral algorithms for linear and nonlinear fluid dynamics stability analyses is greatly expanded. The chapter on spectral algorithms for incompressible flow focuses on algorithms that have proven most useful in practice, has much greater coverage of algorithms for two or more non-periodic directions, and shows how to treat outflow boundaries. Material on spectral methods for compressible flow emphasizes boundary conditions for hyperbolic systems, algorithms for simulation of homogeneous turbulence, and improved methods for shock fitting. This book is a companion to Spectral Methods: Fundamentals in Single Domains.
Spectral Feature Selection For Data Mining Open Access
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Author : Zheng Alan Zhao
language : en
Publisher: CRC Press
Release Date : 2011-12-14
Spectral Feature Selection For Data Mining Open Access written by Zheng Alan Zhao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-14 with Business & Economics categories.
Spectral Feature Selection for Data Mining introduces a novel feature selection technique that establishes a general platform for studying existing feature selection algorithms and developing new algorithms for emerging problems in real-world applications. This technique represents a unified framework for supervised, unsupervised, and semisupervise
Spectral Methods
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Author : Claudio Canuto
language : en
Publisher: Springer
Release Date : 2011-09-07
Spectral Methods written by Claudio Canuto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-07 with Science categories.
Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.
Spectral Clustering And Biclustering
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Author : Marianna Bolla
language : en
Publisher: John Wiley & Sons
Release Date : 2013-06-27
Spectral Clustering And Biclustering written by Marianna Bolla and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-27 with Mathematics categories.
Explores regular structures in graphs and contingency tables by spectral theory and statistical methods This book bridges the gap between graph theory and statistics by giving answers to the demanding questions which arise when statisticians are confronted with large weighted graphs or rectangular arrays. Classical and modern statistical methods applicable to biological, social, communication networks, or microarrays are presented together with the theoretical background and proofs. This book is suitable for a one-semester course for graduate students in data mining, multivariate statistics, or applied graph theory; but by skipping the proofs, the algorithms can also be used by specialists who just want to retrieve information from their data when analysing communication, social, or biological networks. Spectral Clustering and Biclustering: Provides a unified treatment for edge-weighted graphs and contingency tables via methods of multivariate statistical analysis (factoring, clustering, and biclustering). Uses spectral embedding and relaxation to estimate multiway cuts of edge-weighted graphs and bicuts of contingency tables. Goes beyond the expanders by describing the structure of dense graphs with a small spectral gap via the structural eigenvalues and eigen-subspaces of the normalized modularity matrix. Treats graphs like statistical data by combining methods of graph theory and statistics. Establishes a common outline structure for the contents of each algorithm, applicable to networks and microarrays, with unified notions and principles.
Implementing Spectral Methods For Partial Differential Equations
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Author : David A. Kopriva
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-27
Implementing Spectral Methods For Partial Differential Equations written by David A. Kopriva and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-27 with Mathematics categories.
This book explains how to solve partial differential equations numerically using single and multidomain spectral methods. It shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries.
A Spectral Algorithm For Envelope Reduction Of Sparse Matrices
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Author : National Aeronautics and Space Adm Nasa
language : en
Publisher:
Release Date : 2018-10-21
A Spectral Algorithm For Envelope Reduction Of Sparse Matrices written by National Aeronautics and Space Adm Nasa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-21 with categories.
The problem of reordering a sparse symmetric matrix to reduce its envelope size is considered. A new spectral algorithm for computing an envelope-reducing reordering is obtained by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. This Laplacian eigenvector solves a continuous relaxation of a discrete problem related to envelope minimization called the minimum 2-sum problem. The permutation vector computed by the spectral algorithm is a closest permutation vector to the specified Laplacian eigenvector. Numerical results show that the new reordering algorithm usually computes smaller envelope sizes than those obtained from the current standard algorithms such as Gibbs-Poole-Stockmeyer (GPS) or SPARSPAK reverse Cuthill-McKee (RCM), in some cases reducing the envelope by more than a factor of two. Barnard, Stephen T. and Pothen, Alex and Simon, Horst D. Ames Research Center NAS2-12961; NSF CCR-9024954; DE-FG02-91ER25095...
Hyperspectral Data Processing
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Author : Chein-I Chang
language : en
Publisher: John Wiley & Sons
Release Date : 2013-04-08
Hyperspectral Data Processing written by Chein-I Chang and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-08 with Technology & Engineering categories.
Hyperspectral Data Processing: Algorithm Design and Analysis is a culmination of the research conducted in the Remote Sensing Signal and Image Processing Laboratory (RSSIPL) at the University of Maryland, Baltimore County. Specifically, it treats hyperspectral image processing and hyperspectral signal processing as separate subjects in two different categories. Most materials covered in this book can be used in conjunction with the author’s first book, Hyperspectral Imaging: Techniques for Spectral Detection and Classification, without much overlap. Many results in this book are either new or have not been explored, presented, or published in the public domain. These include various aspects of endmember extraction, unsupervised linear spectral mixture analysis, hyperspectral information compression, hyperspectral signal coding and characterization, as well as applications to conceal target detection, multispectral imaging, and magnetic resonance imaging. Hyperspectral Data Processing contains eight major sections: Part I: provides fundamentals of hyperspectral data processing Part II: offers various algorithm designs for endmember extraction Part III: derives theory for supervised linear spectral mixture analysis Part IV: designs unsupervised methods for hyperspectral image analysis Part V: explores new concepts on hyperspectral information compression Parts VI & VII: develops techniques for hyperspectral signal coding and characterization Part VIII: presents applications in multispectral imaging and magnetic resonance imaging Hyperspectral Data Processing compiles an algorithm compendium with MATLAB codes in an appendix to help readers implement many important algorithms developed in this book and write their own program codes without relying on software packages. Hyperspectral Data Processing is a valuable reference for those who have been involved with hyperspectral imaging and its techniques, as well those who are new to the subject.