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.

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...

These 14 papers present mathematical models for different imaging techniques in medicine and non-destructive testing. Readers are given insights into a modern field of scientific computing, with applications leading from the basics to actual research activities.

Dieses Lehrbuch behandelt zunachst den klassischen Stoff wie Riesz- und Fredholmtheorie in funktionalanalytischer Darstellung. Ein Schwerpunkt ist die Anwendung von Methoden und Ergebnissen aus der Theorie der Integralgleichungen auf gewohnliche und partielle Differentialgleichungen. Neben der Behandlung der analytischen Aspekte wird auch auf die numerische Losung von Integralgleichungen eingegangen. Spezifisch fur das Buch sind eine ausfuhrliche Behandlung von Integralgleichungen 1. Art, wie sie bei der Modellierung inverser Probleme auftreten, und ein Kapitel uber nichtlineare...