Sparse Matrix Methods In Optimization

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Direct Methods for Sparse Linear Systems

Author : Timothy A. Davis
Publisher : SIAM
ISBN 13 : 0898716136
Total Pages : 228 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Direct Methods for Sparse Linear Systems by : Timothy A. Davis

Download or read book Direct Methods for Sparse Linear Systems written by Timothy A. Davis and published by SIAM. This book was released on 2006-09-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Sparse matrix methods in optimization

Author : Stanford University. Systems Optimization Laboratory
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Sparse matrix methods in optimization by : Stanford University. Systems Optimization Laboratory

Download or read book Sparse matrix methods in optimization written by Stanford University. Systems Optimization Laboratory and published by . This book was released on 1982 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization algorithms typically require the solution of many systems of linear equations B sub Y sub = b sub. When large numbers of variables or constraints are present, these linear systems could account for much of the total computation time. Both direct and iterative equation solvers are needed in practice. Unfortunately, most of the off-the shelf solvers are designed for single systems, whereas optimization problems give rise to hundreds or thousands of systems. To avoid refactorization, or to speed the convergence of an iterative method, it is essential to note that B sub is related to B sub - 1. The authors review various sparse matrices that arise in optimization, and discuss compromises that are currently being made in dealing with them. Since significant advances continue to be made with single-system solvers they give special attention to methods that allow such solvers to be used repeatedly on a sequence of modified systems (e.g., the product-form update; use of the Schur complement). The speed of factorizing a matrix then becomes relatively less important than the efficiency of subsequent solves with very many right-hand sides. At the same time it is hoped that future improvements to linear-equation software will be oriented more specifically to the case of related matrices B sub k. (Author).

Iterative Methods for Sparse Linear Systems

Author : Yousef Saad
Publisher : SIAM
ISBN 13 : 0898715342
Total Pages : 537 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Iterative Methods for Sparse Linear Systems by : Yousef Saad

Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Sparse Optimization Theory and Methods

Author : Yun-Bin Zhao
Publisher : CRC Press
ISBN 13 : 1351624148
Total Pages : 222 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Sparse Optimization Theory and Methods by : Yun-Bin Zhao

Download or read book Sparse Optimization Theory and Methods written by Yun-Bin Zhao and published by CRC Press. This book was released on 2018-07-04 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seeking sparse solutions of underdetermined linear systems is required in many areas of engineering and science such as signal and image processing. The efficient sparse representation becomes central in various big or high-dimensional data processing, yielding fruitful theoretical and realistic results in these fields. The mathematical optimization plays a fundamentally important role in the development of these results and acts as the mainstream numerical algorithms for the sparsity-seeking problems arising from big-data processing, compressed sensing, statistical learning, computer vision, and so on. This has attracted the interest of many researchers at the interface of engineering, mathematics and computer science. Sparse Optimization Theory and Methods presents the state of the art in theory and algorithms for signal recovery under the sparsity assumption. The up-to-date uniqueness conditions for the sparsest solution of underdertemined linear systems are described. The results for sparse signal recovery under the matrix property called range space property (RSP) are introduced, which is a deep and mild condition for the sparse signal to be recovered by convex optimization methods. This framework is generalized to 1-bit compressed sensing, leading to a novel sign recovery theory in this area. Two efficient sparsity-seeking algorithms, reweighted l1-minimization in primal space and the algorithm based on complementary slackness property, are presented. The theoretical efficiency of these algorithms is rigorously analysed in this book. Under the RSP assumption, the author also provides a novel and unified stability analysis for several popular optimization methods for sparse signal recovery, including l1-mininization, Dantzig selector and LASSO. This book incorporates recent development and the author’s latest research in the field that have not appeared in other books.

Direct Methods for Sparse Matrices

Author : I. S. Duff
Publisher : Oxford University Press
ISBN 13 : 0192507516
Total Pages : 539 pages
Book Rating : 4.1/5 (925 download)

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Book Synopsis Direct Methods for Sparse Matrices by : I. S. Duff

Download or read book Direct Methods for Sparse Matrices written by I. S. Duff and published by Oxford University Press. This book was released on 2017-02-10 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of sparsity is a key to solving large problems in many fields. This second edition is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and complexity; nearly all examples in the first edition were of order less than 5,000 in the first edition, and are often more than a million in the second edition. Computer architectures are now much more complex, requiring new ways of adapting algorithms to parallel environments with memory hierarchies. Because the area is such an important one to all of computational science and engineering, a huge amount of research has been done in the last 30 years, some of it by the authors themselves. This new research is integrated into the text with a clear explanation of the underlying mathematics and algorithms. New research that is described includes new techniques for scaling and error control, new orderings, new combinatorial techniques for partitioning both symmetric and unsymmetric problems, and a detailed description of the multifrontal approach to solving systems that was pioneered by the research of the authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.

Sparse Matrix Computations

Author : James R. Bunch
Publisher : Academic Press
ISBN 13 : 1483263401
Total Pages : 468 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Sparse Matrix Computations by : James R. Bunch

Download or read book Sparse Matrix Computations written by James R. Bunch and published by Academic Press. This book was released on 2014-05-10 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sparse Matrix Computations is a collection of papers presented at the 1975 Symposium by the same title, held at Argonne National Laboratory. This book is composed of six parts encompassing 27 chapters that contain contributions in several areas of matrix computations and some of the most potential research in numerical linear algebra. The papers are organized into general categories that deal, respectively, with sparse elimination, sparse eigenvalue calculations, optimization, mathematical software for sparse matrix computations, partial differential equations, and applications involving sparse matrix technology. This text presents research on applied numerical analysis but with considerable influence from computer science. In particular, most of the papers deal with the design, analysis, implementation, and application of computer algorithms. Such an emphasis includes the establishment of space and time complexity bounds and to understand the algorithms and the computing environment. This book will prove useful to mathematicians and computer scientists.

Direct Methods for Sparse Linear Systems

Author : Timothy A. Davis
Publisher : SIAM
ISBN 13 : 9780898718881
Total Pages : 229 pages
Book Rating : 4.7/5 (188 download)

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Book Synopsis Direct Methods for Sparse Linear Systems by : Timothy A. Davis

Download or read book Direct Methods for Sparse Linear Systems written by Timothy A. Davis and published by SIAM. This book was released on 2006-01-01 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Robust Low-Rank and Sparse Matrix Decomposition

Author : Thierry Bouwmans
Publisher : CRC Press
ISBN 13 : 1498724639
Total Pages : 553 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Handbook of Robust Low-Rank and Sparse Matrix Decomposition by : Thierry Bouwmans

Download or read book Handbook of Robust Low-Rank and Sparse Matrix Decomposition written by Thierry Bouwmans and published by CRC Press. This book was released on 2016-05-27 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Robust Low-Rank and Sparse Matrix Decomposition: Applications in Image and Video Processing shows you how robust subspace learning and tracking by decomposition into low-rank and sparse matrices provide a suitable framework for computer vision applications. Incorporating both existing and new ideas, the book conveniently gives you one-stop access to a number of different decompositions, algorithms, implementations, and benchmarking techniques. Divided into five parts, the book begins with an overall introduction to robust principal component analysis (PCA) via decomposition into low-rank and sparse matrices. The second part addresses robust matrix factorization/completion problems while the third part focuses on robust online subspace estimation, learning, and tracking. Covering applications in image and video processing, the fourth part discusses image analysis, image denoising, motion saliency detection, video coding, key frame extraction, and hyperspectral video processing. The final part presents resources and applications in background/foreground separation for video surveillance. With contributions from leading teams around the world, this handbook provides a complete overview of the concepts, theories, algorithms, and applications related to robust low-rank and sparse matrix decompositions. It is designed for researchers, developers, and graduate students in computer vision, image and video processing, real-time architecture, machine learning, and data mining.

Sparse Solutions of Underdetermined Linear Systems and Their Applications

Author : Ming-Jun Lai
Publisher : SIAM
ISBN 13 : 1611976510
Total Pages : pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Sparse Solutions of Underdetermined Linear Systems and Their Applications by : Ming-Jun Lai

Download or read book Sparse Solutions of Underdetermined Linear Systems and Their Applications written by Ming-Jun Lai and published by SIAM. This book was released on 2021-06-25 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents a special solution to underdetermined linear systems where the number of nonzero entries in the solution is very small compared to the total number of entries. This is called a sparse solution. Since underdetermined linear systems can be very different, the authors explain how to compute a sparse solution using many approaches. Sparse Solutions of Underdetermined Linear Systems and Their Applications contains 64 algorithms for finding sparse solutions of underdetermined linear systems and their applications for matrix completion, graph clustering, and phase retrieval and provides a detailed explanation of these algorithms including derivations and convergence analysis. Exercises for each chapter help readers understand the material. This textbook is appropriate for graduate students in math and applied math, computer science, statistics, data science, and engineering. Advisors and postdoctoral scholars will also find the book interesting and useful.

Splitting Algorithms for Convex Optimization and Applications to Sparse Matrix Factorization

Author : Rong Rong
Publisher :
ISBN 13 :
Total Pages : 95 pages
Book Rating : 4.:/5 (861 download)

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Book Synopsis Splitting Algorithms for Convex Optimization and Applications to Sparse Matrix Factorization by : Rong Rong

Download or read book Splitting Algorithms for Convex Optimization and Applications to Sparse Matrix Factorization written by Rong Rong and published by . This book was released on 2013 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several important applications in machine learning, data mining, signal and image processing can be formulated as the problem of factoring a large data matrix as a product of sparse matrices. Sparse matrix factorization problems are usually solved via alternating convex optimization methods. These methods involve at each iteration a large convex optimization problem with non-differentiable cost and constraint functions, which is typically solved by block coordinate descent algorithm. In this thesis, we investigate first-order algorithms based on forward-backward splitting and Douglas-Rachford splitting algorithms, as an alternative to the block coordinate descent algorithm. We describe efficient methods to evaluate the proximal operators and resolvents needed in the splitting algorithms. We discuss in detail two applications: Structured Sparse Principal Component Analysis and Sparse Dictionary Learning. For these two applications, we compare the splitting algorithms and block coordinate descent on synthetic data and benchmark data sets. Experimental results show that several of the splitting methods, in particular Tseng's modified forward-backward method and the Chambolle-Pock splitting method, are often faster and more accurate than the block coordinate descent algorithm.

Sparse Matrix Technology

Author : Sergio Pissanetzky
Publisher : Academic Press
ISBN 13 : 1483270408
Total Pages : 336 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Sparse Matrix Technology by : Sergio Pissanetzky

Download or read book Sparse Matrix Technology written by Sergio Pissanetzky and published by Academic Press. This book was released on 2014-06-28 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sparse Matrix Technology presents the methods, concepts, ideas, and applications of sparse matrix technology. The text provides the fundamental methods, procedures, techniques, and applications of sparse matrix technology in software development. The book covers topics on storage schemes and computational techniques needed for sparse matrix technology; sparse matrix methods and algorithms for the direct solution of linear equations; and algorithms for different purposes connected with sparse matrix technology. Engineers, programmers, analysts, teachers, and students in the computer sciences will find the book interesting.

Groups, Matrices, and Vector Spaces

Author : James B. Carrell
Publisher : Springer
ISBN 13 : 038779428X
Total Pages : 410 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Groups, Matrices, and Vector Spaces by : James B. Carrell

Download or read book Groups, Matrices, and Vector Spaces written by James B. Carrell and published by Springer. This book was released on 2017-09-02 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable.

Large Sparse Numerical Optimization

Author : Thomas Frederick Coleman
Publisher : Springer
ISBN 13 :
Total Pages : 120 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Large Sparse Numerical Optimization by : Thomas Frederick Coleman

Download or read book Large Sparse Numerical Optimization written by Thomas Frederick Coleman and published by Springer. This book was released on 1984 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Optimization

Author : Boris Teodorovich Poli͡ak
Publisher :
ISBN 13 :
Total Pages : 474 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Introduction to Optimization by : Boris Teodorovich Poli͡ak

Download or read book Introduction to Optimization written by Boris Teodorovich Poli͡ak and published by . This book was released on 1987 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Practical Methods for Optimal Control and Estimation Using Nonlinear Programming

Author : John T. Betts
Publisher : SIAM
ISBN 13 : 0898716888
Total Pages : 442 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Practical Methods for Optimal Control and Estimation Using Nonlinear Programming by : John T. Betts

Download or read book Practical Methods for Optimal Control and Estimation Using Nonlinear Programming written by John T. Betts and published by SIAM. This book was released on 2010-01-01 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: A focused presentation of how sparse optimization methods can be used to solve optimal control and estimation problems.

Sparse Modeling

Author : Irina Rish
Publisher : CRC Press
ISBN 13 : 1439828695
Total Pages : 255 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Sparse Modeling by : Irina Rish

Download or read book Sparse Modeling written by Irina Rish and published by CRC Press. This book was released on 2014-12-01 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sparse models are particularly useful in scientific applications, such as biomarker discovery in genetic or neuroimaging data, where the interpretability of a predictive model is essential. Sparsity can also dramatically improve the cost efficiency of signal processing. Sparse Modeling: Theory, Algorithms, and Applications provides an introduction to the growing field of sparse modeling, including application examples, problem formulations that yield sparse solutions, algorithms for finding such solutions, and recent theoretical results on sparse recovery. The book gets you up to speed on the latest sparsity-related developments and will motivate you to continue learning about the field. The authors first present motivating examples and a high-level survey of key recent developments in sparse modeling. The book then describes optimization problems involving commonly used sparsity-enforcing tools, presents essential theoretical results, and discusses several state-of-the-art algorithms for finding sparse solutions. The authors go on to address a variety of sparse recovery problems that extend the basic formulation to more sophisticated forms of structured sparsity and to different loss functions. They also examine a particular class of sparse graphical models and cover dictionary learning and sparse matrix factorizations.

Sparsity Methods for Systems and Control

Author : Masaaki Nagahara
Publisher :
ISBN 13 : 9781680837247
Total Pages : 220 pages
Book Rating : 4.8/5 (372 download)

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Book Synopsis Sparsity Methods for Systems and Control by : Masaaki Nagahara

Download or read book Sparsity Methods for Systems and Control written by Masaaki Nagahara and published by . This book was released on 2020-09-30 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of sparsity has been attracting a lot of attention in the fields related not only to signal processing, machine learning, and statistics, but also systems and control. The method is known as compressed sensing, compressive sampling, sparse representation, or sparse modeling. More recently, the sparsity method has been applied to systems and control to design resource-aware control systems. This book gives a comprehensive guide to sparsity methods for systems and control, from standard sparsity methods in finite-dimensional vector spaces (Part I) to optimal control methods in infinite-dimensional function spaces (Part II). The primary objective of this book is to show how to use sparsity methods for several engineering problems. For this, the author provides MATLAB programs by which the reader can try sparsity methods for themselves. Readers will obtain a deep understanding of sparsity methods by running these MATLAB programs. Sparsity Methods for Systems and Control is suitable for graduate level university courses, though it should also be comprehendible to undergraduate students who have a basic knowledge of linear algebra and elementary calculus. Also, especially part II of the book should appeal to professional researchers and engineers who are interested in applying sparsity methods to systems and control.