Dynamical Systems Method and Applications: Theoretical Developments and Numerical Examples

Dynamical Systems Method and Applications: Theoretical Developments and Numerical Examples

by Alexander G. Ramm, Nguyen S. Hoang
     
 

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Demonstrates the application of DSM to solve a broad range of operator equations

The dynamical systems method (DSM) is a powerful computational method for solving operator equations. With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed problems. The

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Overview

Demonstrates the application of DSM to solve a broad range of operator equations

The dynamical systems method (DSM) is a powerful computational method for solving operator equations. With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed problems. The authors offer a clear, step-by-step, systematic development of DSM that enables readers to grasp the method's underlying logic and its numerous applications.

Dynamical Systems Method and Applications begins with a general introduction and then sets forth the scope of DSM in Part One. Part Two introduces the discrepancy principle, and Part Three offers examples of numerical applications of DSM to solve a broad range of problems in science and engineering. Additional featured topics include:

  • General nonlinear operator equations

  • Operators satisfying a spectral assumption

  • Newton-type methods without inversion of the derivative

  • Numerical problems arising in applications

  • Stable numerical differentiation

  • Stable solution to ill-conditioned linear algebraic systems

Throughout the chapters, the authors employ the use of figures and tables to help readers grasp and apply new concepts. Numerical examples offer original theoretical results based on the solution of practical problems involving ill-conditioned linear algebraic systems, and stable differentiation of noisy data.

Written by internationally recognized authorities on the topic, Dynamical Systems Method and Applications is an excellent book for courses on numerical analysis, dynamical systems, operator theory, and applied mathematics at the graduate level. The book also serves as a valuable resource for professionals in the fields of mathematics, physics, and engineering.

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Editorial Reviews

From the Publisher
“The book is well organized and presents the DSM method to solve a broad range of operator equations. Suitable for senior under graduate and under graduate students as well as practical engineers and researchers interested in dynamical systems methods and application for operator equations”.  (Zentralblatt MATH, 1 December 2012)

Product Details

ISBN-13:
9781118199602
Publisher:
Wiley, John & Sons, Incorporated
Publication date:
06/07/2013
Sold by:
Barnes & Noble
Format:
NOOK Book
Pages:
576
File size:
37 MB
Note:
This product may take a few minutes to download.

What People are saying about this

From the Publisher
“The book is well organized and presents the DSM method to solve a broad range of operator equations. Suitable for senior under graduate and under graduate students as well as practical engineers and researchers interested in dynamical systems methods and application for operator equations”. (Zentralblatt MATH, 1 December 2012)

Meet the Author

Alexander G. Ramm, PhD, is Professor in the Department of Mathematics at Kansas State University. Dr. Ramm serves as associate editor for several journals.

Nguyen S. Hoang, PhD, is Visiting Assistant Professor in the Department of Mathematics at the University of Oklahoma. He has published numerous journal articles in the areas of numerical analysis, operator theory, ordinary and partial differential equations, optimization, and inverse and ill-posed problems.

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