Dynamical Systems Method and Applications (eBook)

Theoretical Developments and Numerical Examples

Alexander G. Ramm, Nguyen S. Hoang (Autoren)

eBook Download: PDF

2012 | 1. Auflage
576 Seiten
John Wiley & Sons (Verlag)
9781118199596 (ISBN)

Infos

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.

Autor

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.

Inhalt

PART I

1 Introduction 3

2 Ill-posed problems 11

3 DSM for well-posed problems 57

4 DSM and linear ill-posed problems 71

5 Some inequalities 93

6 DSM for monotone operators 133

7 DSM for general nonlinear operator equations 145

8 DSM for operators satisfying a spectral assumption 155

9 DSM in Banach spaces 161

10 DSM and Newton-type methods without inversion of the
derivative 169

11 DSM and unbounded operators 177

12 DSM and nonsmooth operators 181

13 DSM as a theoretical tool 195

14 DSM and iterative methods 201

15 Numerical problems arising in applications 213

PART II

16 Solving linear operator equations by a Newton-type DSM
255

17 DSM of gradient type for solving linear operator equations
269

18 DSM for solving linear equations with finite-rank operators
281

19 A discrepancy principle for equations with monotone
continuous operators 295

20 DSM of Newton-type for solving operator equations with
minimal smoothness assumptions 307

21 DSM of gradient type 347

22 DSM of simple iteration type 373

23 DSM for solving nonlinear operator equations in Banach spaces
409

PART III

24 Solving linear operator equations by the DSM 423

25 Stable solutions of Hammerstein-type integral equations
441

26 Inversion of the Laplace transform from the real axis using
an adaptive iterative method 455

Rezensionen

"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)

Produkt-Details

• Erscheint lt. Verlag: 5.1.2012
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Schlagworte: Chaos / Fractal / Dynamical Systems • Chaos, Fraktale u. dynamische Systeme • Control Systems Technology • Electrical & Electronics Engineering • Elektrotechnik u. Elektronik • Mathematics • Mathematik • Numerical Methods • Numerische Mathematik • numerische Methoden • Regelungstechnik
• ISBN-13: 9781118199596 / 9781118199596