Ill-Posed Problems: Theory and Applications / Edition 1

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This volume presents a unified approach to the solution of ill-posed problems, based on the concept of a regularizing algorithm (RA). This idea is then explored in depth in the discussion of topics such as common conditions for the existence of regularizing algorithms, necessary and sufficient conditions of the approximations for linear problems, and the principle of iterative regularization for nonlinear problems. The majority of these issues have not previously been discussed in a monograph on ill-posed problems. The efficiency of many of the suggested algorithms will prove useful in their application to a wide range of practical problems. This volume can be read by anyone with a basic knowledge of functional analysis.
This book will be of interest to applied mathematicians, engineers, and specialists in inverse problems.

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Editorial Reviews

Presents a unified approach to the solution of ill-posed problems based on the concept of a regularizing algorithm. Discusses in depth such topics as the common conditions for the existence of regularizing algorithms, necessary and sufficient conditions of the approximations for linear problems, and the principle of iterative regularization for nonlinear problems. Addressed to applied mathematicians, engineers, specialists in inverse problems, and other with a good foundation in functional analysis. Not a translation of the authors' work in Russian, but based on it. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780792330738
  • Publisher: Springer Netherlands
  • Publication date: 11/1/2007
  • Series: Mathematics and Its Applications (closed) Series, #301
  • Edition description: 1994
  • Edition number: 1
  • Pages: 258
  • Product dimensions: 0.63 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

Preface. Introduction. 1. General problems of regularizability. 2. Regularizing algorithms on compacta. 3. Tikhonov's scheme for constructing regularizing algorithms. 4. General technique for constructing linear RA for linear problems in Hilbert space. 5. Iterative algorithms for solving nonlinear ill-posed problems with monotonic operators. Principle of iterative regularization. 6. Applications of the principle of iterative regularization. 7. Iterative methods for solving nonlinear ill-posed operator equations with non-monotonic operators. 8. Application of regularizing algorithms to solving practical problems. Bibliography. Index.

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