Dynamical Systems Method for Solving Nonlinear Operator Equations ( Volume 208 )

Publication series :Volume 208

Author: Ramm   Alexander G.  

Publisher: Elsevier Science‎

Publication year: 2006

E-ISBN: 9780080465562

P-ISBN(Paperback): 9780444527950

P-ISBN(Hardback):  9780444527950

Subject: O241 数值分析

Language: ENG

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Description

Dynamical Systems Method for Solving Nonlinear Operator Equations is of interest to graduate students in functional analysis, numerical analysis, and ill-posed and inverse problems especially. The book presents a general method for solving operator equations, especially nonlinear and ill-posed. It requires a fairly modest background and is essentially self-contained. All the results are proved in the book, and some of the background material is also included. The results presented are mostly obtained by the author.

  • Contains a systematic development of a novel general method, the dynamical systems method, DSM for solving operator equations, especially nonlinear and ill-posed
  • Self-contained, suitable for wide audience
  • Can be used for various courses for graduate students and partly for undergraduates (especially for RUE classes)

Chapter

Front Cover

pp.:  1 – 6

Preface

pp.:  6 – 12

Table of Contents

pp.:  12 – 16

Chapter 1 Introduction

pp.:  16 – 24

Chapter 2 Ill-posed problems

pp.:  24 – 76

Chapter 3 DSM for well-posed problems

pp.:  76 – 90

Chapter 4 DSM and linear ill-posed problems

pp.:  90 – 112

Chapter 5 Some inequalities

pp.:  112 – 124

Chapter 6 DSM for monotone operators

pp.:  124 – 136

Chapter 7 DSM for general nonlinear operator equations

pp.:  136 – 148

Chapter 8 DSM for operators satisfying a spectral assumption

pp.:  148 – 156

Chapter 9 DSM in Banach spaces

pp.:  156 – 164

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

pp.:  164 – 174

Chapter 11 DSM and unbounded operators

pp.:  174 – 178

Chapter 12 DSM and nonsmooth operators

pp.:  178 – 192

Chapter 13 DSM as a theoretical tool

pp.:  192 – 198

Chapter 14 DSM and iterative methods

pp.:  198 – 212

Chapter 15 Numerical problems arising in applications

pp.:  212 – 256

Chapter 16 Auxiliary results from analysis

pp.:  256 – 290

Bibliographical notes

pp.:  290 – 294

Bibliography

pp.:  294 – 303

Index

pp.:  303 – 306

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