Sparse Solutions of Underdetermined Linear Systems and Their Applications

Sparse Solutions of Underdetermined Linear Systems and Their Applications
Author: Ming-Jun Lai
Publisher: SIAM
Total Pages:
Release: 2021-06-25
Genre: Mathematics
ISBN: 1611976510

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.

Direct Methods for Sparse Linear Systems

Direct Methods for Sparse Linear Systems
Author: Timothy A. Davis
Publisher: SIAM
Total Pages: 228
Release: 2006-09-01
Genre: Computers
ISBN: 0898716136

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 Applied Linear Algebra

Introduction to Applied Linear Algebra
Author: Stephen Boyd
Publisher: Cambridge University Press
Total Pages: 477
Release: 2018-06-07
Genre: Business & Economics
ISBN: 1316518965

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Ambient Intelligence – Software and Applications – 14th International Symposium on Ambient Intelligence

Ambient Intelligence – Software and Applications – 14th International Symposium on Ambient Intelligence
Author: Paulo Novais
Publisher: Springer Nature
Total Pages: 281
Release: 2023-09-25
Genre: Technology & Engineering
ISBN: 3031434617

This book presents the latest research on Ambient Intelligence (AmI) presented in the 14th International Symposium on Ambient Intelligence (ISAmI 2023). Among others, interested researchers can find works on the recognition of emotions and life conditions; smart applications for improving people’s quality of life and safety; smart cities and territories; as well as advances in data semantics, organization, and privacy, among others. The symposium was organized by the Universidade do Minho (Portugal), the Universitat Politècnica de València (Spain), the University of Granada (Spain), the National Institute of Informatics (Japan), the Instituto Superior de Engenharia do Porto (Portugal), the Universidad de Salamanca (Spain), and with the AIR Institute (Spain) as sponsor. The present edition was hosted by the LASI and Centro Algoritmi of the University of Minho in Guimarães (Portugal) from July 12 to 14, 2023.

Applied Numerical Linear Algebra

Applied Numerical Linear Algebra
Author: James W. Demmel
Publisher: SIAM
Total Pages: 426
Release: 1997-08-01
Genre: Mathematics
ISBN: 0898713897

This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.

Numerical Linear Algebra with Applications

Numerical Linear Algebra with Applications
Author: William Ford
Publisher: Academic Press
Total Pages: 629
Release: 2014-09-14
Genre: Mathematics
ISBN: 0123947847

Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. The text consists of six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra. It explains in great detail the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra. In addition to examples from engineering and science applications, proofs of required results are provided without leaving out critical details. The Preface suggests ways in which the book can be used with or without an intensive study of proofs. This book will be a useful reference for graduate or advanced undergraduate students in engineering, science, and mathematics. It will also appeal to professionals in engineering and science, such as practicing engineers who want to see how numerical linear algebra problems can be solved using a programming language such as MATLAB, MAPLE, or Mathematica. - Six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra - Detailed explanations and examples - A through discussion of the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra - Examples from engineering and science applications

Sparse and Redundant Representations

Sparse and Redundant Representations
Author: Michael Elad
Publisher: Springer Science & Business Media
Total Pages: 376
Release: 2010-08-12
Genre: Mathematics
ISBN: 1441970118

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.