Regularization of Inverse Problems

Heinz Werner Engl, Martin Hanke, A. Neubauer

ISBN 10: 0792361407 / ISBN 13: 9780792361404

Edité par Kluwer Academic Publishers, US, 2000

A propos de cet article

In the last two decades, the field of inverse problems has certainly been one of the fastest growing areas in applied mathematics. This growth has largely been driven by the needs of applications both in other sciences and in industry. In Chapter 1, we will give a short overview over some classes of inverse problems of practical interest. Like everything in this book, this overview is far from being complete and quite subjective. As will be shown, inverse problems typically lead to mathematical models that are not well-posed in the sense of Hadamard, i.e., to ill-posed problems. This means especially that their solution is unstable under data perturbations. Numerical meth­ ods that can cope with this problem are the so-called regularization methods. This book is devoted to the mathematical theory of regularization methods. For linear problems, this theory can be considered to be relatively complete and will be de­ scribed in Chapters 2 - 8. For nonlinear problems, the theory is so far developed to a much lesser extent. We give an account of some of the currently available results, as far as they might be of lasting value, in Chapters 10 and 11. Although the main emphasis of the book is on a functional analytic treatment in the context of operator equations, we include, for linear problems, also some information on numerical aspects in Chapter 9. Softcover reprint of the original 1st ed. 2000.

N° de réf. du vendeur LU-9780792361404

Détails bibliographiques

• Titre: Regularization of Inverse Problems
• Éditeur: Kluwer Academic Publishers, US
• Date de parution: 2000
• Langue: anglais
• ISBN à 10 chiffres: 0792361407
• ISBN à 13 chiffres: 9780792361404
• Reliure: Paperback
• État de l'article: New

A propos de ce titre

Synopsis

In the last two decades, the field of inverse problems has certainly been one of the fastest growing areas in applied mathematics. This growth has largely been driven by the needs of applications both in other sciences and in industry. In Chapter 1, we will give a short overview over some classes of inverse problems of practical interest. Like everything in this book, this overview is far from being complete and quite subjective. As will be shown, inverse problems typically lead to mathematical models that are not well-posed in the sense of Hadamard, i.e., to ill-posed problems. This means especially that their solution is unstable under data perturbations. Numerical meth- ods that can cope with this problem are the so-called regularization methods. This book is devoted to the mathematical theory of regularization methods. For linear problems, this theory can be considered to be relatively complete and will be de- scribed in Chapters 2 - 8. For nonlinear problems, the theory is so far developed to a much lesser extent. We give an account of some of the currently available results, as far as they might be of lasting value, in Chapters 10 and 11. Although the main emphasis of the book is on a functional analytic treatment in the context of operator equations, we include, for linear problems, also some information on numerical aspects in Chapter 9.