Regularization of Inverse Problems

Regularization of Inverse Problems

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This book is devoted to the mathematical theory of regularization methods and gives an account of the currently available results about regularization methods for linear and nonlinear ill-posed problems. Both continuous and iterative regularization methods are considered in detail with special emphasis on the development of parameter choice and stopping rules which lead to optimal convergence rates.
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Product details

  • Hardback | 322 pages
  • 162.6 x 236.2 x 27.9mm | 612.36g
  • Dordrecht, Netherlands
  • English
  • 1996 ed.
  • VIII, 322 p.
  • 0792341570
  • 9780792341574

Table of contents

Preface. 1. Introduction: Examples of Inverse Problems. 2. Ill-Posed Linear Operator Equations. 3. Regularization Operators. 4. Continuous Regularization Methods. 5. Tikhonov Regularization. 6. Iterative Regularization Methods. 7. The Conjugate Gradient Method. 8. Regularization with Differential Operators. 9. Numerical Realization. 10. Tikhonov Regularization of Nonlinear Problems. 11. Iterative Methods for Nonlinear Problems. A. Appendix: A.1. Weighted Polynomial Minimization Problems. A.2. Orthogonal Polynomials. A.3. Christoffel Functions. Bibliography. Index.
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Review quote

`It is written in a very clear style, the material is well organized, and there is an extensive bibliography with 290 items. There is no doubt that this book belongs to the modern standard references on ill-posed and inverse problems. It can be recommended not only to mathematicians interested in this, but to students with a basic knowledge of functional analysis, and to scientists and engineers working in this field.'
Mathematical Reviews Clippings, 97k
`... it will be an extremely valuable tool for researchers in the field, who will find under the same cover and with unified notation material that is otherwise scattered in extremely diverse publications.'
SIAM Review, 41:2 (1999)
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