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Splitting Methods in Communication, Imaging, Science, and Engineering pp 1–17Cite as

Introduction

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Abstract

The main goal of this chapter is to present a brief overview of operator splitting methods and algorithms when applied to the solution of initial value problems and optimization problems, topics to be addressed with many more details in the following chapters of this book. The various splitting algorithms, methods, and schemes to be considered and discussed include: the Lie scheme, the Strang symmetrized scheme, the Douglas-Rachford and Peaceman-Rachford alternating direction methods, the alternating direction method of multipliers (ADMM), and the split Bregman method. This chapter also contains a brief description of (most of) the following chapters of this book.

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Acknowledgements

All the chapters in this book have been peer-reviewed. We greatly appreciate the voluntary work and experted reviews by the anonymous reviewers. We want to express our deep and sincere gratitude to all the authors, who have made tremendous contributions and offered generous support to this book.

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Authors and Affiliations

  1. Department of Mathematics, University of Houston, Houston, TX, 77204, USA

    Roland Glowinski

  2. Department of Mathematics, UCLA, Los Angeles, CA, 90095, USA

    Stanley J. Osher & Wotao Yin

Authors
  1. Roland Glowinski
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  2. Stanley J. Osher
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  3. Wotao Yin
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Correspondence to Roland Glowinski .

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Editors and Affiliations

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

    Roland Glowinski

  2. Department of Mathematics, UCLA, Los Angeles, California, USA

    Stanley J. Osher

  3. Department of Mathematics, UCLA, Los Angeles, California, USA

    Wotao Yin

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Glowinski, R., Osher, S.J., Yin, W. (2016). Introduction. In: Glowinski, R., Osher, S., Yin, W. (eds) Splitting Methods in Communication, Imaging, Science, and Engineering. Scientific Computation. Springer, Cham. https://doi.org/10.1007/978-3-319-41589-5_1

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