Springer International Publishing, Switzerland, 2016. — 822 p. — (Scientific Computation). — ISBN 978-3-319-41587-1.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. Contents -Introduction -Operator-Splitting Schemes for the Time Discretization of Initial Value Problems -Augmented Lagrangian Algorithms and Alternating Direction Methods of Multipliers -Operator-Splitting Methods for the Direct Numerical Simulation of Particulate Flow -Operator-Splitting Methods for the Numerical Solution of Nonlinear Problems from Condensate and Plasma Physics -Optimal FPR Rate and Arbitrarily Slow Convergence -Nonconvex Sparse Regularization and Splitting Algorithms -ADMM and Non-convex Variational Problems -Operator Splitting Methods in Compressive Sensing and Sparse Approximation -First Order Algorithms in Variational Image Processing -A Parameter Free ADI-Like Method for the Numerical Solution of Large Scale Lyapunov Equations -Splitting Enables Overcoming the Curse of Dimensionality -ADMM Algorithmic Regularization Paths for Sparse Statistical Machine Learning -Decentralized Learning for Wireless Communications and Networking -Splitting Methods for SPDEs: From Robustness to Financial Engineering, Optimal Control, and Nonlinear Filtering -Application of Operator Splitting Methods in Finance -A Numerical Method to Solve Multi-Marginal Optimal Transport Problems with Coulomb Cost -Robust Split-Step Fourier Methods for Simulating the Propagation of Ultra-Short Pulses in Single- and Two-Mode Optical Communication Fibers -Operator Splitting Methods with Error Estimator and Adaptive Time-Stepping. Application to the Simulation of Combustion Phenomena -Splitting Methods for Some Nonlinear Wave Problems -Operator Splitting Algorithms for Free Surface Flows: Application to Extrusion Processes -An Operator Splitting Approach to the Solution of Fluid-Structure Interaction Problems in Hemodynamics -On Circular Cluster Formation in a Rotating Suspension of Non-Brownian Settling Particles in a -Fully Filled Circular Cylinder: An Operator Splitting Approach to the Numerical Simulation
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