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.

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.

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).

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 Matrices

Author : Iain S. Duff
Publisher : Oxford University Press
ISBN 13 : 0198508387
Total Pages : 451 pages
Book Rating : 4.1/5 (985 download)

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

Download or read book Direct Methods for Sparse Matrices written by Iain S. Duff and published by Oxford University Press. This book was released on 2017 with total page 451 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 book provides both insight and answers for those attempting to solve these problems.

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.

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.

Groups, Matrices, and Vector Spaces

Author : James B. Carrell
Publisher : Springer
ISBN 13 : 038779428X
Total Pages : 415 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 415 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.

Computational Methods for Large Sparse Power Systems Analysis

Author : S.A. Soman
Publisher : Springer Science & Business Media
ISBN 13 : 1461508231
Total Pages : 349 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Computational Methods for Large Sparse Power Systems Analysis by : S.A. Soman

Download or read book Computational Methods for Large Sparse Power Systems Analysis written by S.A. Soman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational methods in Power Systems require significant inputs from diverse disciplines, such as data base structures, numerical analysis etc. Strategic decisions in sparsity exploitation and algorithm design influence large-scale simulation and high-speed computations. Selection of programming paradigm shapes the design, its modularity and reusability. This has a far reaching effect on software maintenance. Computational Methods for Large Sparse Power Systems Analysis: An Object Oriented Approach provides a unified object oriented (OO) treatment for power system analysis. Sparsity exploitation techniques in OO paradigm are emphasized to facilitate large scale and fast computing. Specific applications like large-scale load flow, short circuit analysis, state estimation and optimal power flow are discussed within this framework. A chapter on modeling and computational issues in power system dynamics is also included. Motivational examples and illustrations are included throughout the book. A library of C++ classes provided along with this book has classes for transmission lines, transformers, substation etc. A CD-ROM with C++ programs is also included. It contains load flow, short circuit analysis and network topology processor applications. Power system data is provided and systems up to 150 buses can be studied. Other Special Features: This book is the first of its kind, covering power system applications designed with an OO perspective. Chapters on object orientation for modeling of power system computations, data structure, large sparse linear system solver, sparse QR decomposition in an OO framework are special features of this book.

The Linear Algebra a Beginning Graduate Student Ought to Know

Author : Jonathan S. Golan
Publisher : Springer Science & Business Media
ISBN 13 : 1402054955
Total Pages : 443 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis The Linear Algebra a Beginning Graduate Student Ought to Know by : Jonathan S. Golan

Download or read book The Linear Algebra a Beginning Graduate Student Ought to Know written by Jonathan S. Golan and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book rigorously deals with the abstract theory and, at the same time, devotes considerable space to the numerical and computational aspects of linear algebra. It features a large number of thumbnail portraits of researchers who have contributed to the development of linear algebra as we know it today and also includes over 1,000 exercises, many of which are very challenging. The book can be used as a self-study guide; a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level; or as a reference book.

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.

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.

Modelling, Simulation and Optimization of Integrated Circuits

Author : Kurt Antreich
Publisher : Springer Science & Business Media
ISBN 13 : 9783764321925
Total Pages : 386 pages
Book Rating : 4.3/5 (219 download)

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Book Synopsis Modelling, Simulation and Optimization of Integrated Circuits by : Kurt Antreich

Download or read book Modelling, Simulation and Optimization of Integrated Circuits written by Kurt Antreich and published by Springer Science & Business Media. This book was released on 2003 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: In November 2001 the Mathematical Research Center at Oberwolfach, Germany, hosted the third Conference on Mathematical Models and Numerical Simulation in Electronic Industry. It brought together researchers in mathematics, electrical engineering and scientists working in industry.The contributions to this volume try to bridge the gap between basic and applied mathematics, research in electrical engineering and the needs of industry.

Matrix Methods: Theory, Algorithms And Applications - Dedicated To The Memory Of Gene Golub

Author : Vadim Olshevsky
Publisher : World Scientific
ISBN 13 : 9814469556
Total Pages : 604 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Matrix Methods: Theory, Algorithms And Applications - Dedicated To The Memory Of Gene Golub by : Vadim Olshevsky

Download or read book Matrix Methods: Theory, Algorithms And Applications - Dedicated To The Memory Of Gene Golub written by Vadim Olshevsky and published by World Scientific. This book was released on 2010-04-05 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compared to other books devoted to matrices, this volume is unique in covering the whole of a triptych consisting of algebraic theory, algorithmic problems and numerical applications, all united by the essential use and urge for development of matrix methods. This was the spirit of the 2nd International Conference on Matrix Methods and Operator Equations from 23-27 July 2007 in Moscow that was organized by Dario Bini, Gene Golub, Alexander Guterman, Vadim Olshevsky, Stefano Serra-Capizzano, Gilbert Strang and Eugene Tyrtyshnikov.Matrix methods provide the key to many problems in pure and applied mathematics. However, linear algebra theory, numerical algorithms and matrices in FEM/BEM applications usually live as if in three separate worlds. In this volume, maybe for the first time ever, they are compiled together as one entity as it was at the Moscow meeting, where the algebraic part was impersonated by Hans Schneider, algorithms by Gene Golub, and applications by Guri Marchuk. All topics intervened in plenary sessions are specially categorized into three sections of this volume.The soul of the meeting was Gene Golub, who rendered a charming “Golub's dimension” to the three main axes of the conference topics. This volume is dedicated in gratitude to his memory.

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:

Optimization Algorithms on Matrix Manifolds

Author : P.-A. Absil
Publisher : Princeton University Press
ISBN 13 : 1400830249
Total Pages : 240 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Optimization Algorithms on Matrix Manifolds by : P.-A. Absil

Download or read book Optimization Algorithms on Matrix Manifolds written by P.-A. Absil and published by Princeton University Press. This book was released on 2009-04-11 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.