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Splitting Methods in Communication, Imaging, Science, and Engineering

  • Book
  • © 2016

Overview

Editors:
  1. Roland Glowinski

    1. Department of Mathematics, University of Houston, Houston, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Stanley J. Osher

    1. Department of Mathematics, UCLA, Los Angeles, USA

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  3. Wotao Yin

    1. Department of Mathematics, UCLA, Los Angeles, USA

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • No other book on splitting methods published in the last 10 years
  • Includes applications that cover a wide variety of scientific areas
  • Editors and authors include top international researchers in multiple areas
  • Includes supplementary material: sn.pub/extras

Part of the book series: Scientific Computation (SCIENTCOMP)

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Table of contents (23 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Introduction

    • Roland Glowinski, Stanley J. Osher, Wotao Yin
    Pages 1-17

  3. Some Facts About Operator-Splitting and Alternating Direction Methods

    • Roland Glowinski, Tsorng-Whay Pan, Xue-Cheng Tai
    Pages 19-94

  4. Operator Splitting

    • Shev MacNamara, Gilbert Strang
    Pages 95-114

  5. Convergence Rate Analysis of Several Splitting Schemes

    • Damek Davis, Wotao Yin
    Pages 115-163

  6. Self Equivalence of the Alternating Direction Method of Multipliers

    • Ming Yan, Wotao Yin
    Pages 165-194

  7. Application of the Strictly Contractive Peaceman-Rachford Splitting Method to Multi-Block Separable Convex Programming

    • Bingsheng He, Han Liu, Juwei Lu, Xiaoming Yuan
    Pages 195-235

  8. Nonconvex Sparse Regularization and Splitting Algorithms

    • Rick Chartrand, Wotao Yin
    Pages 237-249

  9. ADMM and Non-convex Variational Problems

    • Roland Glowinski
    Pages 251-299

  10. Operator Splitting Methods in Compressive Sensing and Sparse Approximation

    • Tom Goldstein, Xiaoqun Zhang
    Pages 301-343

  11. First Order Algorithms in Variational Image Processing

    • M. Burger, A. Sawatzky, G. Steidl
    Pages 345-407

  12. A Parameter Free ADI-Like Method for the Numerical Solution of Large Scale Lyapunov Equations

    • Danny C. Sorensen
    Pages 409-425

  13. Splitting Enables Overcoming the Curse of Dimensionality

    • Jérôme Darbon, Stanley J. Osher
    Pages 427-432

  14. ADMM Algorithmic Regularization Paths for Sparse Statistical Machine Learning

    • Yue Hu, Eric C. Chi, Genevera I. Allen
    Pages 433-459

  15. Decentralized Learning for Wireless Communications and Networking

    • Georgios B. Giannakis, Qing Ling, Gonzalo Mateos, Ioannis D. Schizas, Hao Zhu
    Pages 461-497

  16. Splitting Methods for SPDEs: From Robustness to Financial Engineering, Optimal Control, and Nonlinear Filtering

    • Christian Bayer, Harald Oberhauser
    Pages 499-539

  17. Application of Operator Splitting Methods in Finance

    • Karel in’t Hout, Jari Toivanen
    Pages 541-575

  18. A Numerical Method to Solve Multi-Marginal Optimal Transport Problems with Coulomb Cost

    • Jean-David Benamou, Guillaume Carlier, Luca Nenna
    Pages 577-601

  19. Robust Split-Step Fourier Methods for Simulating the Propagation of Ultra-Short Pulses in Single- and Two-Mode Optical Communication Fibers

    • Ralf Deiterding, Stephen W. Poole
    Pages 603-625

  20. Operator Splitting Methods with Error Estimator and Adaptive Time-Stepping. Application to the Simulation of Combustion Phenomena

    • Stéphane Descombes, Max Duarte, Marc Massot
    Pages 627-641
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Keywords

About this book

This book is about computational methods based on operator splitting.   It consists of twenty-three chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the cross-fertilization of ideas.  

Editors and Affiliations

  • Department of Mathematics, University of Houston, Houston, USA

    Roland Glowinski

  • Department of Mathematics, UCLA, Los Angeles, USA

    Stanley J. Osher, Wotao Yin

About the editors

Roland Glowinski works in Computational Mechanics and Physics and more generally in areas involving the numerical solution of partial differential equations and inequalities. Stanley Osher is a Professor of Mathematics, Computer Science and Electrical Engineering at UCLA, and is an Associate Director of the NSF funded Institute for Pure and Applied Mathematics. Wotao Yin works in optimization theory, develops many fast algorithms for compressive sensing, image processing, medical imaging, wireless networking, etc.

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