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Dynamical Systems Method and Applications: Theoretical Developments and Numerical Examples / Edition 1

Dynamical Systems Method and Applications: Theoretical Developments and Numerical Examples / Edition 1

by Alexander G. Ramm, Nguyen S. Hoang
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Product Details

ISBN-13: 9781118024287
Publisher: Wiley
Publication date: 12/20/2011
Edition description: New Edition
Pages: 576
Product dimensions: 6.20(w) x 9.30(h) x 1.40(d)

About 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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Table of Contents


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


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


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

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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)

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