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Inverse and IllPosed Problems Ser. ; v.36 

Inverse and IllPosed Problems Ser

附註 
Intro  Preface to the Second Edition  Preface  Contents  Introduction  Chapter 1. Wellposedness of problems  1.1. Problem formulation. Hadamard's concept of wellposedness  1.2. Examples of illposed problems  1.3. Tikhonov's concept of wellposedness. Sets of wellposedness  1.4. Stability theorems and their applications  1.5. Normal solvability of operator equations  1.6. Quasisolutions on compact and boundedly compact sets  Chapter 2. Regularizing family of operators  2.1. Pointwise and uniform regularization of operator equations  2.2. Geometric theorems on structure of boundedly compact sets  2.3. Uniform regularization of equations with completely continuous operators  2.4. Structure of sets of uniform regularization in Hilbert spaces  2.5. Sets of uniform regularization for continuous operators  Chapter 3. Basic techniques for constructing regularizing algorithms  3.1. Reduction to operator equations of the second kind  3.2. Method of quasisolutions  3.3. Tikhonov's method of regularization  3.4. Method of residual  3.5. On relations between variational methods  3.6. Generalized method of residual  3.7. Method based on the Picard theorem  3.8. Iterative methods  3.9. Regularization of the Fredholm integral equations of the first kind  3.10. Regularization methods for differential equations  Chapter 4. Optimality and stability of methods for solving illposed problems. Error estimation  4.1. Classification of illposed problems and the concept of an optimal method  4.2. Lower estimate for error of the optimal method  4.3. Error of the regularization method  4.4. Algorithmic peculiarities of the generalized method of residual  4.5. Error of the quasisolution method  4.6. The regularization method with the parameter a satisfying the residual principle 

4.7. Investigation of the simplest scheme of the Lavrent'ev method  4.8. The method of projective regularization  4.9. Calculation of the module of continuity  Chapter 5. Determination of values of unbounded operators  5.1. A unified approach to the solution of illposed problems  5.2. Multivalued linear operators and their properties  5.3. Determination of normal values of linear operators by variational methods  5.4. The best approximation of unbounded operators  5.5. Optimal regularization of the problem of evaluating a derivative in the space C(∞, ∞)  Chapter 6. Finitedimensional approximation of regulirizing algorithms  6.1. The concept of runiform convergence of linear operators  6.2. A general scheme of the finitedimensional approximation  6.3. Application of the general scheme  6.4. Projection method  6.5. Necessary and sufficient conditions for convergence of the projection method  6.6. Error estimation  6.7. Numerical applications  Bibliography  Additional Bibliography to the Second Edition  Comments to Additional Bibliography  Index 

The Inverse and IllPosed Problems Series is a series of monographs publishing postgraduate level information on inverse and illposed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology 

Description based on publisher supplied metadata and other sources 

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries 
鏈接 
Print version: Ivanov, Valentin K. Theory of Linear IllPosed Problems and Its Applications
Berlin/Boston : De Gruyter, Inc.,c2002 9789067643672

主題 
Operator equations.;Integral operators.;Numerical analysis  Improperly posed problems


Electronic books

Alt Author 
Vasin, Vladimir V


Tanana, Vitalii P

