Sparse Solutions Of Underdetermined Linear Systems And Their Applications PDF Download
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Author | : Ming-Jun Lai |
Publisher | : SIAM |
Total Pages | : |
Release | : 2021-06-25 |
Genre | : Mathematics |
ISBN | : 1611976510 |
Download Sparse Solutions of Underdetermined Linear Systems and Their Applications Book in PDF, ePub and Kindle
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.
Author | : Yousef Saad |
Publisher | : SIAM |
Total Pages | : 537 |
Release | : 2003-04-01 |
Genre | : Mathematics |
ISBN | : 0898715342 |
Download Iterative Methods for Sparse Linear Systems Book in PDF, ePub and Kindle
Mathematics of Computing -- General.
Author | : Yaakov Tsaig |
Publisher | : |
Total Pages | : 154 |
Release | : 2007 |
Genre | : |
ISBN | : 9780549063803 |
Download Sparse Solution of Underdetermined Linear Systems Book in PDF, ePub and Kindle
Next, we introduce Stagewise Orthogonal Matching Pursuit (StOMP), a rapid iterative method to find sparse approximate solutions to underdetermined linear systems. We demonstrate that StOMP is much faster than competing approaches to recover sparse solutions, and at the same time, its ability to recover the sparsest solution is comparable with that of ℓ1 minimization.
Author | : Timothy A. Davis |
Publisher | : SIAM |
Total Pages | : 228 |
Release | : 2006-09-01 |
Genre | : Computers |
ISBN | : 0898716136 |
Download Direct Methods for Sparse Linear Systems Book in PDF, ePub and Kindle
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.
Author | : Amir Z. Averbuch |
Publisher | : |
Total Pages | : |
Release | : 2011 |
Genre | : Geology |
ISBN | : 9783642277931 |
Download Handbook of Geomathematics Book in PDF, ePub and Kindle
Author | : Michael Elad |
Publisher | : Springer Science & Business Media |
Total Pages | : 376 |
Release | : 2010-08-12 |
Genre | : Mathematics |
ISBN | : 1441970118 |
Download Sparse and Redundant Representations Book in PDF, ePub and Kindle
A long long time ago, echoing philosophical and aesthetic principles that existed since antiquity, William of Ockham enounced the principle of parsimony, better known today as Ockham’s razor: “Entities should not be multiplied without neces sity. ” This principle enabled scientists to select the ”best” physical laws and theories to explain the workings of the Universe and continued to guide scienti?c research, leadingtobeautifulresultsliketheminimaldescriptionlength approachtostatistical inference and the related Kolmogorov complexity approach to pattern recognition. However, notions of complexity and description length are subjective concepts anddependonthelanguage“spoken”whenpresentingideasandresults. The?eldof sparse representations, that recently underwent a Big Bang like expansion, explic itly deals with the Yin Yang interplay between the parsimony of descriptions and the “language” or “dictionary” used in them, and it became an extremely exciting area of investigation. It already yielded a rich crop of mathematically pleasing, deep and beautiful results that quickly translated into a wealth of practical engineering applications. You are holding in your hands the ?rst guide book to Sparseland, and I am sure you’ll ?nd in it both familiar and new landscapes to see and admire, as well as ex cellent pointers that will help you ?nd further valuable treasures. Enjoy the journey to Sparseland! Haifa, Israel, December 2009 Alfred M. Bruckstein vii Preface This book was originally written to serve as the material for an advanced one semester (fourteen 2 hour lectures) graduate course for engineering students at the Technion, Israel.
Author | : Stephen Boyd |
Publisher | : Cambridge University Press |
Total Pages | : 477 |
Release | : 2018-06-07 |
Genre | : Business & Economics |
ISBN | : 1316518965 |
Download Introduction to Applied Linear Algebra Book in PDF, ePub and Kindle
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Author | : Andrew Gordon Wilcox |
Publisher | : |
Total Pages | : 80 |
Release | : 2010 |
Genre | : Algebras, Linear |
ISBN | : |
Download Finding a Sparse Solution of a Linear System with Applications to Coding Theory and Statistics Book in PDF, ePub and Kindle
Author | : M. Vidyasagar |
Publisher | : SIAM |
Total Pages | : 341 |
Release | : 2019-12-03 |
Genre | : Technology & Engineering |
ISBN | : 161197612X |
Download An Introduction to Compressed Sensing Book in PDF, ePub and Kindle
Compressed sensing is a relatively recent area of research that refers to the recovery of high-dimensional but low-complexity objects from a limited number of measurements. The topic has applications to signal/image processing and computer algorithms, and it draws from a variety of mathematical techniques such as graph theory, probability theory, linear algebra, and optimization. The author presents significant concepts never before discussed as well as new advances in the theory, providing an in-depth initiation to the field of compressed sensing. An Introduction to Compressed Sensing contains substantial material on graph theory and the design of binary measurement matrices, which is missing in recent texts despite being poised to play a key role in the future of compressed sensing theory. It also covers several new developments in the field and is the only book to thoroughly study the problem of matrix recovery. The book supplies relevant results alongside their proofs in a compact and streamlined presentation that is easy to navigate. The core audience for this book is engineers, computer scientists, and statisticians who are interested in compressed sensing. Professionals working in image processing, speech processing, or seismic signal processing will also find the book of interest.
Author | : James W. Demmel |
Publisher | : SIAM |
Total Pages | : 426 |
Release | : 1997-08-01 |
Genre | : Mathematics |
ISBN | : 0898713897 |
Download Applied Numerical Linear Algebra Book in PDF, ePub and Kindle
This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.