Lx B Laplacian Solvers And Their Algorithmic Applications
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Lx B Laplacian Solvers And Their Algorithmic Applications
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Author : Nisheeth K Vishnoi
language : en
Publisher:
Release Date : 2013-03-01
Lx B Laplacian Solvers And Their Algorithmic Applications written by Nisheeth K Vishnoi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-01 with categories.
Illustrates the emerging paradigm of employing Laplacian solvers to design novel fast algorithms for graph problems through a small but carefully chosen set of examples. This monograph can be used as the text for a graduate-level course, or act as a supplement to a course on spectral graph theory or algorithms.
Lx B
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Author : Nisheeth K. Vishnoi
language : en
Publisher:
Release Date : 2013
Lx B written by Nisheeth K. Vishnoi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.
In this monograph, the emerging paradigm of employing Laplacian solvers to design new fast algorithms for graph problems is illustrated through a small but carefully chosen set of examples. A significant part of this monograph is also dedicated to developing the ideas that go into the construction of near-linear time Laplacian solvers.
Lx
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Author : Nisheeth K. Vishnoi
language : en
Publisher:
Release Date : 2013
Lx written by Nisheeth K. Vishnoi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Graph theory categories.
The ability to solve a system of linear equations lies at the heart of areas such as optimization, scientific computing, and computer science, and has traditionally been a central topic of research in the area of numerical linear algebra. An important class of instances that arise in practice has the form Lx=b, where L is the Laplacian of an undirected graph. After decades of sustained research and combining tools from disparate areas, we now have Laplacian solvers that run in time nearly linear in the sparsity (that is, the number of edges in the associated graph) of the system, which is a distant goal for general systems. Surprisingly, and perhaps not the original motivation behind this line of research, Laplacian solvers are impacting the theory of fast algorithms for fundamental graph problems. In this monograph, the emerging paradigm of employing Laplacian solvers to design novel fast algorithms for graph problems is illustrated through a small but carefully chosen set of examples. A part of this monograph is also dedicated to developing the ideas that go into the construction of near-linear-time Laplacian solvers. An understanding of these methods, which marry techniques from linear algebra and graph theory, will not only enrich the tool-set of an algorithm designer but will also provide the ability to adapt these methods to design fast algorithms for other fundamental problems.
Integer Programming And Combinatorial Optimization
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Author : Jens Vygen
language : en
Publisher: Springer Nature
Release Date :
Integer Programming And Combinatorial Optimization written by Jens Vygen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Foundations Of Data Science
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Author : Avrim Blum
language : en
Publisher: Cambridge University Press
Release Date : 2020-01-23
Foundations Of Data Science written by Avrim Blum and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-23 with Computers categories.
Covers mathematical and algorithmic foundations of data science: machine learning, high-dimensional geometry, and analysis of large networks.
Direct Methods For Sparse Linear Systems
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Author : Timothy A. Davis
language : en
Publisher: SIAM
Release Date : 2006-09-01
Direct Methods For Sparse Linear Systems written by Timothy A. Davis and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-01 with Computers categories.
The sparse backslash book. Everything you wanted to know but never dared to ask about modern direct linear solvers. Chen Greif, Assistant Professor, Department of Computer Science, University of British Columbia.Overall, the book is magnificent. It fills a long-felt need for an accessible textbook on modern sparse direct methods. Its choice of scope is excellent John Gilbert, Professor, Department of Computer Science, University of California, Santa Barbara.Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages.With a strong emphasis on MATLAB and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.Audience This invaluable book is essential to computational scientists and software developers who want to understand the theory and algorithms behind modern techniques used to solve large sparse linear systems. The book also serves as an excellent practical resource for students with an interest in combinatorial scientific computing.Preface; Chapter 1: Introduction; Chapter 2: Basic algorithms; Chapter 3: Solving triangular systems; Chapter 4: Cholesky factorization; Chapter 5: Orthogonal methods; Chapter 6: LU factorization; Chapter 7: Fill-reducing orderings; Chapter 8: Solving sparse linear systems; Chapter 9: CSparse; Chapter 10: Sparse matrices in MATLAB; Appendix: Basics of the C programming language; Bibliography; Index.
Introduction To High Performance Scientific Computing
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Author : Victor Eijkhout
language : en
Publisher: Lulu.com
Release Date : 2010
Introduction To High Performance Scientific Computing written by Victor Eijkhout and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.
This is a textbook that teaches the bridging topics between numerical analysis, parallel computing, code performance, large scale applications.
Modern Algorithms Of Cluster Analysis
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Author : Slawomir Wierzchoń
language : en
Publisher: Springer
Release Date : 2017-12-29
Modern Algorithms Of Cluster Analysis written by Slawomir Wierzchoń and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-29 with Technology & Engineering categories.
This book provides the reader with a basic understanding of the formal concepts of the cluster, clustering, partition, cluster analysis etc. The book explains feature-based, graph-based and spectral clustering methods and discusses their formal similarities and differences. Understanding the related formal concepts is particularly vital in the epoch of Big Data; due to the volume and characteristics of the data, it is no longer feasible to predominantly rely on merely viewing the data when facing a clustering problem. Usually clustering involves choosing similar objects and grouping them together. To facilitate the choice of similarity measures for complex and big data, various measures of object similarity, based on quantitative (like numerical measurement results) and qualitative features (like text), as well as combinations of the two, are described, as well as graph-based similarity measures for (hyper) linked objects and measures for multilayered graphs. Numerous variants demonstrating how such similarity measures can be exploited when defining clustering cost functions are also presented. In addition, the book provides an overview of approaches to handling large collections of objects in a reasonable time. In particular, it addresses grid-based methods, sampling methods, parallelization via Map-Reduce, usage of tree-structures, random projections and various heuristic approaches, especially those used for community detection.
Faster Algorithms Via Approximation Theory
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Author : Sushant Sachdeva
language : en
Publisher:
Release Date : 2014-03-28
Faster Algorithms Via Approximation Theory written by Sushant Sachdeva and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-28 with Computers categories.
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.
Accuracy And Stability Of Numerical Algorithms
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Author : Nicholas J. Higham
language : en
Publisher: SIAM
Release Date : 2002-01-01
Accuracy And Stability Of Numerical Algorithms written by Nicholas J. Higham and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.