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作者 Ivanov, Valentin K
書名 Theory of Linear Ill-Posed Problems and Its Applications
出版項 Berlin/Boston : De Gruyter, Inc., 2002
國際標準書號 9783110944822 (electronic bk.)
book jacket
說明 1 online resource (295 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
系列 Inverse and Ill-Posed Problems Ser. ; v.36
Inverse and Ill-Posed Problems Ser
附註 Intro -- Preface to the Second Edition -- Preface -- Contents -- Introduction -- Chapter 1. Well-posedness of problems -- 1.1. Problem formulation. Hadamard's concept of well-posedness -- 1.2. Examples of ill-posed problems -- 1.3. Tikhonov's concept of well-posedness. Sets of well-posedness -- 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 ill-posed problems. Error estimation -- 4.1. Classification of ill-posed 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 ill-posed 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. Finite-dimensional approximation of regulirizing algorithms -- 6.1. The concept of r-uniform convergence of linear operators -- 6.2. A general scheme of the finite-dimensional 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 Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed 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 Ill-Posed 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
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