Muutke küpsiste eelistusi

Dynamical Systems Method for Solving Nonlinear Operator Equations, Volume 208 [Kõva köide]

(Kansas State University, Manhattan, KS, USA)
  • Formaat: Hardback, 304 pages, kõrgus x laius: 229x152 mm, kaal: 600 g
  • Sari: Mathematics in Science & Engineering
  • Ilmumisaeg: 25-Sep-2006
  • Kirjastus: Elsevier Science Ltd
  • ISBN-10: 0444527958
  • ISBN-13: 9780444527950
Teised raamatud teemal:
  • Kõva köide
  • Hind: 172,00 €*
  • * saadame teile pakkumise kasutatud raamatule, mille hind võib erineda kodulehel olevast hinnast
  • See raamat on trükist otsas, kuid me saadame teile pakkumise kasutatud raamatule.
  • Kogus:
  • Lisa ostukorvi
  • Tasuta tarne
  • Lisa soovinimekirja
Dynamical Systems Method for Solving Nonlinear Operator Equations, Volume 208Suurem pilt
  • Formaat: Hardback, 304 pages, kõrgus x laius: 229x152 mm, kaal: 600 g
  • Sari: Mathematics in Science & Engineering
  • Ilmumisaeg: 25-Sep-2006
  • Kirjastus: Elsevier Science Ltd
  • ISBN-10: 0444527958
  • ISBN-13: 9780444527950
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780444527950.html
Märksõnad:
The book 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)

Muu info

The book is of interest to graduate students in functional analysis, numerical analysis, and ill-posed and inverse problems especially. While presenting a general method for solving operator equations, especially nonlinear and ill-posed, it requires a fairly modest background and is essentially self-contained
Preface v
Contents xi
Introduction
1(8)
What this book is about
1(1)
What the DSM (Dynamical Systems Method) is
2(1)
The scope of the DSM
3(4)
A discussion of DSM
7(1)
Motivations
8(1)
Ill-posed problems
9(52)
Basic definitions. Examples
9(21)
Variational regularization
30(11)
Quasisolutions
41(4)
Iterative regularization
45(4)
Quasiinversion
49(3)
Dynamical systems method (DSM)
52(4)
Variational regularization for nonlinear equations
56(5)
DSM for well-posed problems
61(14)
Every solvable well-posed problem can be solved by DSM
61(5)
DSM and Newton-type methods
66(2)
DSM and the modified Newton's method
68(1)
DSM and Gauss-Newton-type methods
68(1)
DSM and the gradient method
69(1)
DSM and the simple iterations method
70(1)
DSM and minimization methods
71(2)
Ulm's method
73(2)
DSM and linear ill-posed problems
75(22)
Equations with bounded operators
75(9)
Another approach
84(6)
Equations with unbounded operators
90(1)
Iterative methods
91(3)
Stable calculation of values of unbounded operators
94(3)
Some inequalities
97(12)
Basic nonlinear differential inequality
97(5)
An operator inequality
102(1)
A nonlinear inequality
103(4)
The Gronwall-type inequalities
107(2)
DSM for monotone operators
109(12)
Auxiliary results
109(6)
Formulation of the results and proofs
115(3)
The case of noisy data
118(3)
DSM for general nonlinear operator equations
121(12)
Formulation of the problem. The results and proofs
121(4)
Noisy data
125(2)
Iterative solution
127(3)
Stability of the iterative solution
130(3)
DSM for operators satisfying a spectral assumption
133(8)
Spectral assumption
133(3)
Existence of a solution to a nonlinear equation
136(5)
DSM in Banach spaces
141(8)
Well-posed problems
141(2)
Ill-posed problems
143(2)
Singular perturbation problem
145(4)
DSM and Newton-type methods without inversion of the derivative
149(10)
Well-posed problems
149(3)
Ill-posed problems
152(7)
DSM and unbounded operators
159(4)
Statement of the problem
159(2)
Ill-posed problems
161(2)
DSM and nonsmooth operators
163(14)
Formulation of the results
163(8)
Proofs
171(6)
DSM as a theoretical tool
177(6)
Surjectivity of nonlinear maps
177(1)
When is a local homeomorphism a global one?
178(5)
DSM and iterative methods
183(14)
Introduction
183(1)
Iterative solution of well-posed problems
184(2)
Iterative solution of ill-posed equations with monotone operator
186(4)
Iterative methods for solving nonlinear equations
190(3)
Ill-posed problems
193(4)
Numerical problems arising in applications
197(44)
Stable numerical differentiation
197(8)
Stable differentiation of piecewise-smooth functions
205(12)
Simultaneous approximation of a function and its derivative by interpolation polynomials
217(7)
Other methods of stable differentiation
224(4)
DSM and stable differentiation
228(7)
Stable calculating singular integrals
235(6)
Auxiliary results from analysis
241(34)
Contraction mapping principle
241(5)
Existence an uniqueness of the local solution to the Cauchy problem
246(4)
Derivatives of nonlinear mappings
250(4)
Implicit function theorem
254(2)
An existence theorem
256(2)
Continuity of solutions to operator equations with respect to a parameter
258(5)
Monotone operators in Banach spaces
263(3)
Existence of solutions to operator equations
266(5)
Compactness of embeddings
271(4)
Bibliographical notes 275(4)
Bibliography 279(9)
Index 288