Solving Nonlinear Equations with Iterative Methods
Solving Nonlinear Equations with Iterative Methods

Author: C. T. Kelley

Publisher: SIAM

Published: 2022-10-31

Total Pages: 201

ISBN-13: 1611977266

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This user-oriented guide describes state-of-the-art methods for nonlinear equations and shows, via algorithms in pseudocode and Julia with several examples, how to choose an appropriate iterative method for a given problem and write an efficient solver or apply one written by others. A sequel to the author’s Solving Nonlinear Equations with Newton’s Methods (SIAM, 2003), this book contains new material on pseudo-transient continuation, mixed-precision solvers, and Anderson acceleration. It is supported by a Julia package and a suite of Jupyter notebooks and includes examples of nonlinear problems from many disciplines. This book is will be useful to researchers who solve nonlinear equations, students in numerical analysis, and the Julia community.

Implicit Filtering
Implicit Filtering

Author: C. T. Kelley

Publisher: SIAM

Published: 2011-01-01

Total Pages: 184

ISBN-13: 9781611971903

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Implicit filtering is a way to solve bound-constrained optimization problems for which derivative information is not available. Unlike methods that use interpolation to reconstruct the function and its higher derivatives, implicit filtering builds upon coordinate search and then interpolates to get an approximation of the gradient. The author describes the algorithm, its convergence theory, and a new MATLAB implementation, and includes three case studies. This book is unique in that it is the only one in the area of derivative-free or sampling methods and is accompanied by publicly available software. It is also designed as a software manual and as a reference for implicit filtering - one can approach the book as a consumer of the software, as a student, or as a researcher in sampling and derivative-free methods. The book includes a chapter on convergence theory that is both accessible to students and an overview of recent results on optimization of noisy functions, including results that depend on non-smooth analysis and results on the handling of constraints. Implicit filtering is used in applications in electrical, civil, and mechanical engineering.

Interval Methods for Solving Nonlinear Constraint Satisfaction, Optimization and Similar Problems
Interval Methods for Solving Nonlinear Constraint Satisfaction, Optimization and Similar Problems

Author: Bartłomiej Jacek Kubica

Publisher: Springer

Published: 2019-03-08

Total Pages: 156

ISBN-13: 3030137953

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This book highlights recent research on interval methods for solving nonlinear constraint satisfaction, optimization and similar problems. Further, it presents a comprehensive survey of applications in various branches of robotics, artificial intelligence systems, economics, control theory, dynamical systems theory, and others. Three appendices, on the notation, representation of numbers used as intervals’ endpoints, and sample implementations of the interval data type in several programming languages, round out the coverage.

Practice of Clinical Echocardiography E-Book
Practice of Clinical Echocardiography E-Book

Author: Catherine M. Otto

Publisher: Elsevier Health Sciences

Published: 2016-11-09

Total Pages: 1027

ISBN-13: 0323482422

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The new edition of Practice of Clinical Echocardiography provides expert guidance on interpreting echocardiographic images and Doppler flow data. Designed for those already equipped with a mastery of basic principles, this definitive reference shows you how to apply these findings to your daily clinical decision making. Each chapter focuses on a specific disease process with technical details of qualitative and quantitative interpretation of echocardiographic images and Doppler flow data. Disease-oriented chapters emphasize the role of echocardiography in clinical decision making and prediction of clinical outcomes. New chapters cover emerging technologies, including transcatheter procedures for structural heart disease. Numerous images illustrate findings, while diagrams explain pathophysiology and flow charts guide clinical practice. Each chapter includes a summary box with a practical approach to echo data acquisition, measurement, and interpretation.

Mathematical Image Processing
Mathematical Image Processing

Author: Kristian Bredies

Publisher: Springer

Published: 2019-02-06

Total Pages: 473

ISBN-13: 3030014584

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This book addresses the mathematical aspects of modern image processing methods, with a special emphasis on the underlying ideas and concepts. It discusses a range of modern mathematical methods used to accomplish basic imaging tasks such as denoising, deblurring, enhancing, edge detection and inpainting. In addition to elementary methods like point operations, linear and morphological methods, and methods based on multiscale representations, the book also covers more recent methods based on partial differential equations and variational methods. Review of the German Edition: The overwhelming impression of the book is that of a very professional presentation of an appropriately developed and motivated textbook for a course like an introduction to fundamentals and modern theory of mathematical image processing. Additionally, it belongs to the bookcase of any office where someone is doing research/application in image processing. It has the virtues of a good and handy reference manual. (zbMATH, reviewer: Carl H. Rohwer, Stellenbosch)

Parallel Processing and Applied Mathematics
Parallel Processing and Applied Mathematics

Author: Roman Wyrzykowski

Publisher: Springer Nature

Published: 2020-03-19

Total Pages: 511

ISBN-13: 303043222X

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The two-volume set LNCS 12043 and 12044 constitutes revised selected papers from the 13th International Conference on Parallel Processing and Applied Mathematics, PPAM 2019, held in Bialystok, Poland, in September 2019. The 91 regular papers presented in these volumes were selected from 161 submissions. For regular tracks of the conference, 41 papers were selected from 89 submissions. The papers were organized in topical sections named as follows: Part I: numerical algorithms and parallel scientific computing; emerging HPC architectures; performance analysis and scheduling in HPC systems; environments and frameworks for parallel/distributed/cloud computing; applications of parallel computing; parallel non-numerical algorithms; soft computing with applications; special session on GPU computing; special session on parallel matrix factorizations. Part II: workshop on language-based parallel programming models (WLPP 2019); workshop on models algorithms and methodologies for hybrid parallelism in new HPC systems; workshop on power and energy aspects of computations (PEAC 2019); special session on tools for energy efficient computing; workshop on scheduling for parallel computing (SPC 2019); workshop on applied high performance numerical algorithms for PDEs; minisymposium on HPC applications in physical sciences; minisymposium on high performance computing interval methods; workshop on complex collective systems. Chapters "Parallel adaptive cross approximation for the multi-trace formulation of scattering problems" and "A High-Order Discontinuous Galerkin Solver with Dynamic Adaptive Mesh Refinement to Simulate Cloud Formation Processes" of LNCS 12043 are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.