Ramm / Hoang Dynamical Systems Method and Applications

Theoretical Developments and Numerical Examples
1. Auflage 2012
ISBN: 978-1-118-19959-6
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 576 Seiten, E-Book

Demonstrates the application of DSM to solve a broad range ofoperator equations
The dynamical systems method (DSM) is a powerful computationalmethod for solving operator equations. With this book as theirguide, readers will master the application of DSM to solve avariety of linear and nonlinear problems as well as ill-posed andwell-posed problems. The authors offer a clear, step-by-step,systematic development of DSM that enables readers to grasp themethod's underlying logic and its numerous applications.
Dynamical Systems Method and Applications begins with ageneral introduction and then sets forth the scope of DSM in PartOne. Part Two introduces the discrepancy principle, and Part Threeoffers examples of numerical applications of DSM to solve a broadrange of problems in science and engineering. Additional featuredtopics 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 figuresand tables to help readers grasp and apply new concepts. Numericalexamples offer original theoretical results based on the solutionof practical problems involving ill-conditioned linear algebraicsystems, and stable differentiation of noisy data.
Written by internationally recognized authorities on the topic,Dynamical Systems Method and Applications is an excellentbook for courses on numerical analysis, dynamical systems, operatortheory, and applied mathematics at the graduate level. The bookalso serves as a valuable resource for professionals in the fieldsof mathematics, physics, and engineering.

Autoren/Hrsg.

Ramm, Alexander G.

Hoang, Nguyen S.

Inhaltsverzeichnis

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 thederivative 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 DSM255
17 DSM of gradient type for solving linear operator equations269
18 DSM for solving linear equations with finite-rank operators281
19 A discrepancy principle for equations with monotonecontinuous operators 295
20 DSM of Newton-type for solving operator equations withminimal 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 spaces409
PART III
24 Solving linear operator equations by the DSM 423
25 Stable solutions of Hammerstein-type integral equations441
26 Inversion of the Laplace transform from the real axis usingan adaptive iterative method 455

Über Autor(innen)

Alexander G. Ramm, PhD, is Professor in the Department ofMathematics at Kansas State University. Dr. Ramm serves asassociate editor for several journals.
Nguyen S. Hoang, PhD, is Visiting Assistant Professor inthe Department of Mathematics at the University of Oklahoma. He haspublished numerous journal articles in the areas of numericalanalysis, operator theory, ordinary and partial differentialequations, optimization, and inverse and ill-posed problems.